New Semester Started Get 50% OFF Study Help! --h --m --s Claim Now

Question Answers

Textbooks

Find textbooks, questions and answers

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Study Help
Tutors
AI Study Planner NEW
Sell Books

Search
Sign In
Register

study help
mathematics
cambridge international as & a level mathematics probability & statistics

Cambridge International AS & A Level Mathematics Probability & Statistics 1 Coursebook 1st Edition Dean Chalmers, Julian Gilbey - Solutions

Weiqi has two fair triangular spinners. The sides of one spinner are labelled 1, 2, 3, and the sides of the other are labelled 2, 3, 4. Weiqi spins them simultaneously and notes the two numbers on which they come to rest.a. Find the probability that these two numbers differ by 1.b. Weiqi spins both
Let T be the number of times that a fair coin is tossed, up to and including the toss on which the first tail is obtained. Find the mode and the mean of T.
On average, Diya concedes one penalty in every six hockey matches that she plays. Find the probability that Diya next concedes a penalty:a. In the eighth match that she plays b. After the fourth match that she plays.
Given that X ~ B(n, p), E(X ) = 20 and Var(X ) = 12, find:a. The value of n and of pb. P(X = 21).
Given that B~B(8, 2/7), find:a. P(V = 4)b. P(V ≥ 7)c. P(V ≤ 2)d. P(3 ≤ V < 6)e. P(V is an odd number).
One plastic robot is given away free inside each packet of a certain brand of biscuits. There are four colours of plastic robot (red, yellow, blue and green) and each colour is equally likely to occur. Nick buys some packets of these biscuits. Find the probability that i. He gets a green robot
Given that S ~ Geo( p) and that E(S) 4 1/2 = , find P(S = 2).
The probability that Mike is shown a yellow card in any football match that he plays is 1/2. Find the probability that Mike is next shown a yellow card:a. In the third match that he playsb. Before the fourth match that he plays.
Given that Y ~ B(11, 0.23), calculate:a. P(Y ≠ 3)b. P[Y < E(Y )].
Given that W ~B(9, 0.32), find:a. P(W = 5)b. P(W ≠ 5)c. P(W < 2)d. P(0
A family has booked a long holiday in Skragness, where the probability of rain on any particular day is 0.3.Find the probability that:a. The first day of rain is on the third day of their holidayb. It does not rain for the first 2 weeks of their holiday.
The random variable Y follows a geometric distribution. Given that P(Y = 1) = 0.2, find E(Y ).
Given that T ~ Geo(0.32), find:a. P(T = 3)b. P(T ≤ 6)c. P(T > 7) .
Given that X ~ B(8,0.25), calculate:a. E(X ) and Var(X )b. P[X = E(X )] c. P[X < E(X )].
Given that Y ~B(7, 0.6), find:a. P(Y = 7)b. P(Y = 5)c. P(Y ≠ 4)d. P(3
Given that X~ B(n, 1/n) find an expression for P(X = 1) in terms of n.
Given that X ~ Geo(0.36), find the exact value of E(X ).
Given the discrete random variable X ~ Geo(0.2), find:a. P(X = 7)b. P(X ≠ 5)c. P(X > 4) .
Calculate the expectation, variance and standard deviation of each of the following discrete random variables. Give non-exact answers correct to 3 significant figures.a. V ~ B(5, 0.2)b. W ~ B(24, 0.55)c. X ~ B(365, 0.18)d. Y ~ B(20, 0.5)
The variable X has a binomial distribution with n = 4 and p = 0.2. Find:a. P(X = 4)b. P(X = 0)c. P(X = 3)d. P(X = 3 or 4).
The probability that a boy succeeds with each basketball shot is 7/9. He takes two shots and the discrete random variable S represents the number of successful shots.Show that P(S = 0) = 4/81 and draw up the probability distribution table for S.
Five grapes are randomly selected without replacement from a bag containing one red grape and six green grapes.Name and list the possible values of two discrete random variables in this situation.State the relationship between the values of your two variables.
Find the mean and the variance of the discrete random variable X, whose probability distribution is given in the following table. 1 2 3 P(X =x) 1-k 2- 3k 3-4k 4- 6k %3D
The discrete random variable V is such that V ∈{1, 2, 3}. Given that P(V = 1) = P(V = 2) = 2 × P(V = 3), draw up the probability distribution table for V.
The probability distribution for the random variable X is given in the following table.Calculate E(X ) and Var(X ). 2 3 P(X = x) 0.10 0.12 0.36 0.42
The following table shows the probability distribution for the random variable Y.a. Given that Var(Y) = 1385.2, show that q2 – 61q + 624 = 0 and solve this equation.b. Find the greatest possible value of E(Y). 1 10 101 P(Y = y) 0.2 0.4 0.2 0.2
The probability distribution for the random variable X is given in the following table.Find the value of p and work out P(2 < X < 5). 2. 3 4 P(X = x) P 2p 3p %3D in
The probability distribution for the random variable Y is given in the following table.a. Find the value of p.b. Calculate E(Y ) and the standard deviation of Y. 1 2 3 4 P(Y= 0.03 2p 0.32 0.05
An investment company has produced the following table, which shows the probabilities of various percentage profits on money invested over a period of 3 years.a. Calculate the expected profit on an investment of $50000.b. A woman considers investing $50000 with the company, but decides that her
The probability distribution for the random variable W is given in the following table.a. Form an equation using k, then solve it.b. Explain why only one of your solutions is valid.c. Find P(6 ≤ W< 10) . 6. 9. 12 15 k P(W = w) 2k k? 13 2 -3k 5 50
The random variable T is such that T ∈{1, 3, 6,10}. Given that the four possible values of T are equiprobable, find E(T) and Var(T).
A chef wishes to decorate each of four cupcakes with one randomly selected sweet. They choose the sweets at random from eight toffees, three chocolates and one jelly. Find the variance of the number of cupcakes that will be decorated with a chocolate sweet.
The following table shows the probability distribution for the random variable V.Given that E(V) = 5.38, find the value of m and calculate Var(V). 1 3 9. P(V = v) 0.4 0.28 0.14 0.18
The faces of a biased die are numbered 1, 2, 3, 4, 5 and 6. The random variable X is the score when the die is thrown. The probability distribution table for X is given.The die is thrown 3 times. Find the probability that the score is at least 4 on at least 1 of the 3 throws. 1 3 4 6. Cam P P P P
R is a random variable such that R ∈{10, 20, 70,100}. Given that P(R = r) is proportional to r, show that E(R) = 77 and find Var(R).
At a garden centre, there is a display of roses: 25 are red, 20 are white, 15 are pink and 5 are orange. Three roses are chosen at random.a. Show that the probability of selecting three red roses is approximately 0.0527.b. Draw up the probability distribution table for the number of red roses
A picnic basket contains five jars: one of marmalade, two of peanut butter and two of jam. A boy removes one jar at random from the basket and then his sister takes two jars, both selected at random.a. Find the probability that the sister selects her jars from a basket that contains:i. Exactly one
Three vehicles from a company’s six trucks, five vans, three cars and one motorbike are randomly selected and tested for roadworthiness.a. Show that the probability of selecting three vans is 2/91.b. Draw up the probability distribution table for the number of vans selected.c. Find the
The probability distribution for the random variable W is given in the following table.Given that E(W) = a, find a and evaluate Var(W). 7 a 24 P(W = 0.3 0.3 ab 0.1 0.3
Two ordinary fair dice are rolled. The product and the sum of the two numbers obtained are calculated.The score awarded, S, is equal to the absolute (i.e. non-negative) difference between the product and the sum.For example, if 5 and 3 are rolled, then S = (5 × 3) − (5 + 3) = 7.a. State the
The possible outcomes from a business venture are graded from 5 to 1, as shown in the following table.a. Calculate the expected grade and use it to describe the expected outcome of the venture. Find the standard deviation and explain what it gives a measure of in this case.b. Investigate the
A fair triangular spinner has sides labelled 0,1 and 2, and another fair triangular spinner has sides labelled –1, 0 and 1. The score, X, is equal to the sum of the squares of the two numbers on which the spinners come to rest.a. List the five possible values of X.b. Draw up the probability
A pack of five DVDs contains three movies and two documentaries. Three DVDs are selected and the following table shows the probability distribution for M, the number of movies selected.Draw up the probability distribution table for D, the number of documentaries selected. 1 2 3 P(M 0.3 0.6 0.1 qure
Two ordinary fair dice are rolled. The discrete random variable X is the lowest common multiple of the two numbers rolled.a. Draw up the probability distribution table for X.b. Find E(X ) and P[X > E(X)].c. Calculate Var(X).
A discrete random variable X, where X ∈{2, 3, 4, 5}, is such that P(X = x) = (b – x)2/30a. Calculate the two possible values of b.b. Hence, find P(2 < X < 5).
In a particular country, 90% of the population is right-handed and 40% of the population has red hair. Two people are randomly selected from the population. Draw up the probability distribution for X, the number of right-handed, red-haired people selected, and state what assumption must be made in
In a game, a player attempts to hit a target by throwing three darts. With each throw, a player has a 30% chance of hitting the target.a. Draw up the probability distribution table for H, the number of times the target is hit in a game.b. How many times is the target expected to be hit in 1000
Two students are randomly selected from a class of 12 girls and 18 boys.a. Find the expected number of girls and the expected number of boys.b. Write the ratio of the expected number of girls to the expected number of boys in simplified form. What do you notice about this ratio?c. Calculate the
Set A consists of the ten digits 0, 0, 0, 0, 0, 0, 2, 2, 2, 4.Set B consists of the seven digits 0, 0, 0, 0, 2, 2, 2.One digit is chosen at random from each set. The random variable X is defined as the sum of these two digits.i. Show that P(X = 2) = 3/7.ii. Tabulate the probability distribution of
A fair 4-sided die, numbered 1, 2, 3 and 5, is rolled twice. The random variable X is the sum of the two numbers on which the die comes to rest.a. Show that P(X = 8) = 1/8.b. Draw up the probability distribution table for X, and find P(X > 6).
A sewing basket contains eight reels of cotton: four are green, three are red and one is yellow. Three reels of cotton are randomly selected from the basket.a. Show that the expected number of yellow cotton reels is 0.375.b. Find the expected number of red cotton reels.c. Hence, state the expected
The discrete random variable Y is such that Y ∈{4, 5, 8,14,17} and P(Y = y) is directly proportional to 1/y + 1. Find P(Y > 4).
There are eight letters in a post box, and five of them are addressed to Mr Nut. Mr Nut removes four letters at random from the box.a. Find the probability that none of the selected letters are addressed to Mr Nut.b. Draw up the probability distribution table for N, the number of selected letters
A company offers a $1000 cash loan to anyone earning a monthly salary of at least $2000. To secure the loan, the borrower signs a contract with a promise to repay the $1000 plus a fixed fee before 3 months have elapsed. Failure to do this gives the company a legal right to take $1540 from the
X is a discrete random variable and X ∈{0, 1, 2, 3}. Given that P(X > 1) = 0.24, P(0 < X < 3) = 0.5 and P(X = 0 or 2) = 0.62, find P(X ≤ 2 |X > 0).
A discrete random variable Y is such that Y ∈{8, 9, 10}. Given that P(Y = y) = ky, find the value of the constant k.
When a scout group of 8 juniors and 12 seniors meets on a Monday evening, one scout is randomly selected to hoist a flag. Let the variable X represent the number of juniors selected over n consecutive Monday evenings.a. By drawing up the probability distribution table for X, or otherwise, show that
Four students are to be selected at random from a group that consists of seven boys and x girls. The variables B and G are, respectively, the number of boys selected and the number of girls selected.a. Given that P(B = 1) = P(B = 2), find the value of x.b. Given that G ≠ 3, find the probability
Q is a discrete random variable and Q ∈{3, 4, 5, 6}.a. Given that P(Q = q) = cq2, find the value of the constant c.b. Hence, find P(Q > 4).
An ordinary fair die is rolled. If the die shows an odd number then S, the score awarded, is equal to that number. If the die shows an even number, then the die is rolled again. If on the second roll it shows an odd number, then that is the score awarded. If the die shows an even number on the
A box contains 2 green apples and 2 red apples. Apples are taken from the box, one at a time, without replacement. When both red apples have been taken, the process stops. The random variable X is the number of apples which have been taken when the process stops.i. Show that P(X = 3) = 1/3.ii. Draw
Four books are randomly selected from a box containing 10 novels, 10 reference books and 5 dictionaries.The random variable N represents the number of novels selected.a. Find the value of P(N = 2), correct to 3 significant figures.b. Without further calculation, state which of N = 0 or N = 4 is
A fair 4-sided spinner with sides labelled A, B, B, B is spun four times.a. Show that there are six equally likely ways to obtain exactly two Bs with the four spins.b. By drawing up the probability distribution table for X, the number of times the spinner comes to rest on B, find the value of
In a particular discrete probability distribution the random variable X takes the value 120/r with probability r/45, where r takes all integer values from 1 to 9 inclusive.i. Show that P(X = 40) = 1/15.ii. Construct the probability distribution table for X.iii. Which is the modal value of X?iv.
In a game, a fair 4-sided spinner with edges labelled 0, 1, 2 and 3 is spun. If a player spins 1, 2 or 3, then that is their score. If a player scores 0, then they spin a fair triangular spinner with edges labelled 0,1 and 2, and the number they spin is their score. Let the variable X represent a
A biased coin is tossed three times. The probability distribution for H, the number of heads obtained, is shown in the following table.a. Find the probability of obtaining a head each time the coin is tossed.b. Give another discrete random variable that is related to these trials, and calculate the
Two ordinary fair dice are rolled. A score of 3 points is awarded if exactly one die shows an odd number and there is also a difference of 1 between the two numbers obtained. A player who rolls two even numbers is awarded a score of 2 points, otherwise a player scores 1 point.a. Draw up the
The discrete random variable R is such that R ∈{1, 3, 5, 7}a. Given that P(R = r) = k(r + 1)/r + 2, find the value of the constant k.b. Hence, find P(R ≤ 4).
Find how many of the arrangements of four letters from A, B, C, D, E and F:a. Begin with the letter A b. Contain the letter A.
A book of poetry contains seven poems, three of which are illustrated. In how many different orders can all the poems be read if no two illustrated poems are read one after the other?
Find the number of ways that seven goats and four sheep can sleep in a row if:a. All the goats must sleep next to each otherb. No two sheep may sleep next to each other.
A radio presenter has enough time at the end of their show to play five songs. She has 13 songs by four groups to choose from: five songs by The Anvils, four by The Braziers, three by The Chisels and one by The Dustbins. Find the number of ways she can choose five songs to play if she
Students enrolling at an A Level college must select three different subjects to study from the six that are available. One subject must be chosen from each of the option groups A, B and C, as shown in the following table.a. One student has chosen to study History and Mathematics. How many subjects
A teacher is looking for 6 pupils to appear in the school play and has decided to select them at random from a group of 11 girls and 13 boys.a. Find the number of ways in which the teacher can select the 6 pupils.b. Two roles in the play must be played by girls; three roles must be played by boys,
Five people are randomly selected from a group of 67 women and 33 men. Find the probability that the selection consists of an odd number of women.
Four ordinary fair dice are arranged in a row. Find the number of ways in which this can be done if the four numbers showing on top of the dice:a. Are all oddb. Have a sum that is less than 7.
At company V, 12.5% of the employees have a university degree. At company W, 85% of the employees do not have a university degree. There are 112 employees at company V and 120 employees at company W.a. One employee is randomly selected. Find the probability that they:i. Work for company Vii. Have a
One hundred qualified drivers are selected at random. Out of these 100 drivers, of the 40 drivers who wear spectacles, 30 passed their driving test at the first attempt. Altogether, 25 of the drivers did not pass at their first attempt.a. Show the data given about the drivers in a clearly labelled
A conference hall has 24 overhead lights. Pairs of lights are operated by switches next to the main entrance, and each switch has three numbered settings: 0 (off), 1 (dim), 2 (bright). Find the number of possible lighting arrangements in the hall if: a. There are no restrictionsb. Two
Twelve chairs in two colours are arranged, as shown.Find in how many ways nine people can sit on these chairs if:a. The two blue chairs in column C must remain unoccupiedb. All of the green chairs must be occupiedc. More blue chairs than green chairs must be occupiedd. At least one of the chairs in
In a certain country, vehicle registration plates consist of seven characters: a letter, followed by a three digit number, followed by three letters.For example: B 474 PQRThe first letter cannot be a vowel; the three-digit number cannot begin with 0; and the first of the last three letters cannot
Seats for the guests at an awards ceremony are arranged in two rows of eight and ten, divided by an aisle, as shownSeats are randomly allocated to 18 guests.a. Find the probability that two particular guests are allocated seats:i. On the same side of the aisleii. In the same rowiii. On the same
Find the number of distinct five-letter arrangements that can be made from:a. Two As and three Bs b. Two identical vowels and three Bsc. Two identical vowels and any three identical consonants.
Find the number of distinct arrangements that can be made from all the letters in the word THEATRE when the arrangement:a. Begins with two Ts and ends with two Es b. Has H as its middle letterc. Ends with the three vowels E, A and E.
From a set of 10 rings, a jeweller wishes to display seven of them in their shop window. The formation of the display is shown in the diagram opposite. Find the number of possible displays if, from the set of 10:a. The ring with the largest diamond must go at the top of the displayb. The most
A bag contains six red fuses, five blue fuses and four yellow fuses. Find how many ways there are to select:a. Three fuses of different colours b. Three fuses of the same colourc. 10 fuses in exactly two colours d. Nine fuses in exactly two colours.
Five clowns each have a red wig and a blue wig, which they are all equally likely to wear at any particular time. Find the probability that, at any particular time:a. Exactly two clowns are wearing red wigs b. More clowns are wearing blue wigs than red wigs.
Find how many ways 15 children can be divided into three groups of five if:a. There are no restrictionsb. Two of the children are brothers who must be in the same group.
The following diagram shows a row of post boxes with the owners’ names beneath.Five parcels, one for the owner of each box, have arrived at the post office. If one parcel is randomly placed in each box, find the number of ways in which:a. The five parcels can all be placed in the correct boxesb.
Using each digit not more than once, how many even four-digit numbers can be made from the digits 1, 2, 3, 4, 5, 6 and 7?
The diagram opposite shows the activities offered to children at a school camp.If children must choose three activities to fill their day, how many sets of three activities are there to choose from?
A gardener has nine rose bushes to plant: three have red flowers and six have yellow flowers. If they plant them in a row in random order, find the probability that:a. A yellow rose bush is in the middle of the rowb. The three red rose bushes are not separatedc. No two red rose bushes are next to
An entertainer has been asked to give a performance consisting of four items. They know three songs, five jokes, two juggling tricks and can play one tune on the mandolin. Find how many different ways there are for them to choose the four items if:a. There are no restrictions on their performanceb.
There are x boys and y girls to be arranged in a line. Find the relationship between x and y if it is not possible to separate all the boys.
Find how many three-digit numbers can be made from the digits 0, 1, 2, 3 and 4, used at most once each, if the three-digit number:a. Must be a multiple of 10 b. Cannot begin with zero.
A fair triangular spinner with sides numbered 1, 2 and 3 is spun three times and the numbers that it comes to rest on are written down from left to right to form a three-digit number.a. How many possible three-digit numbers are there?b. Find the probability that the three-digit number is: i.
Two taxis are hired to take a group of eight friends to the airport. One taxi can carry five passengers and the other can carry three passengers.What information is given in this situation by the fact that 8C5 = 8C3 = 56?
A farmer has 50 animals. They have 24 sheep, of which three are male, and they have 26 cattle, of which 20 are female. A veterinary surgeon wishes to test six randomly selected animals. Find the probability that the selection consists of:a. Equal numbers of cattle and sheep b. More females
From a group of nine people, five are to be chosen at random to serve on a committee. In how many ways can this be done if two particular people refuse to serve on the committee together?
Give an example of a practical situation where the calculation nPr = 120 might arise.

Showing 1500 - 1600 of 1990

First
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

Step by Step Answers

Services

Sitemap
Fun
Definitions
Become Tutor
Used Textbooks
Study Help Categories
Recent Questions
Expert Questions
Campus Wear
Sell Your Books

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship
Online Quiz
Give Feedback, Get Rewards

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Student Discount
Campus Ambassador

Secure Payment

Download Our App

© 2026 SolutionInn. All Rights Reserved