1. A standard dice is rolled. What is the probability that a 2, 4, OR 6 will be rolled?

2. Rosa will toss a fair coin twice. If you know that the first

coin toss resulted in heads, what would the probability be that both coins

would land on heads?

3. A spinner is divided into 3 equal sections, with sections

labeled 1, 2, and 3. What is the probability of spinning a 3 on the spinner if

you know the arrow landed on an odd number?

4. A party host gives a door prize to one guest chosen at

random. There are 48 men and 42 women at the party. What is the probability

that the prize goes to a woman? P = 42 90 = 7 15

5. A spinner is divided into five equal sections numbered 1

through 5. The arrow is equally likely to land on any section. (a) Find the

probability table, which is also called the discrete "probability density

function" (or pdf). (b) Calculate the expected value E(X) (or mean x) of

the probability experiment. (c) Calculate the variance V (X) of the probability

experiment. (d) Calculate the standard deviation.

6)

Alaska license plates have two letters followed by three

numbers. What is the probability that a randomly chosen license plate will have

an NC with the number ending in a 3?

7. A 20-sided is rolled. If the result is 10 or less, the

20-sided die is rolled again. If the result is 11 or more, a 4-sided die is

rolled. In either case, the results are summed after the second die roll. What

is the probability that the sum will be 14?

8. Police plan to enforce speed limits during the morning rush

hour on four different routes into the city. The traps on routes A, B, C, and D

are operated 40% , 30%, 20%, and 30% of the time, respectively. Biff always

speeds to work, and he has probability 0.2, 0.1, 0.5, and 0.2 of using those

routes. (a) What is the probability that he'll get a ticket on any one morning?

9. In an urn are 5 blue, 3 red, and 2 yellow marbles. If you

draw 3 marbles, what is the probability that less than 2 will be red if: (a)

You draw with replacement? (b) You draw without replacement?

10) Butch will miss an important TV program while taking

his statistics exam, so he sets both his VCRs to record it. The first one

records 70% of the time, and the second one records 60% of the time. What is

the probability that he gets home after the exam and finds?

(a) No copies of his program? (b) One copy of his program?

(c) Two copies of his program? (d) Good grief, a VCR? What's

that?

11. Two squares are chosen at random on a chessboard. What is

the probability that they have a side in common?

12. At a baby shower, we started discussing baby statistics. One

of the women told us she had heard a report that for every 100 babies born,

there were 6 more boys than girls.

(a) If we were to randomly pick a child from a representative

group, what is the probability of picking a girl?

(b) If we were to pick 10 babies at random, what is the

probability that at least half of them would be girls?

(c) If we were to pick 10 babies at random, what is the

probability that exactly 8 of them would be girls?

(d) If we were to pick 10 babies at random, what is the

probability that no more than 8 of them would be boys?

13. There are an equal number of pennies, nickels, dimes, and

quarters in a bag. What is the probability that the combined value of the four

coins randomly selected with replacement will be $0.41?

14. A quarter, two dimes, a nickel and four pennies are placed

in a bag and mixed thoroughly. Two coins are drawn at random without

replacement, and their total monetary value is recorded. probability table (pdf) for this probability

experiment, and then calculate the expected value, variance and standard

deviation. Coins PP PN NN DP DN DD QP QN QD QQ x .02 .06 .10 .11 .15 .2 .26 .30

.35 .50 p(x) ( 4 2) ( 8 2) = 6 28 41 28 0 42 28 21 28 1 28 41 28 1 28 21

28 0

15 From past experience it is known that 3% of accounts in a

large accounting population are in error. Joe is given a randomized list of

accounts to audit. What is the probability that he audits 5 accurate accounts

before he finds the 6th account in error?

16. An oil company conducts a geological study that indicates

that an exploratory oil well in a certain region should have a 20% chance of

striking oil. What is the probability that the first strike comes on the third

well drilled? The company wants three working rigs in the region. What is the

probability that they can have to drill 8 times or fewer to get the three they

need?

. 17. What is the probability of getting a license plate that

has a repeated letter or digit if you live in a state where the license plate

scheme is four letters followed by two number

. 18. On a multiple-choice test of 10 questions, each question

has 5 possible answers. A student is certain of the answers to 4 questions but

is totally baffled by 6 questions. If the student randomly guesses the answers

to those 6 questions, what is the proba that the student will get a score of 5

or more on the test? Express your answer correct to two decimal places.

19. On a multiple-choice test of 10 questions, each question has

5 possible answers. A student is certain of the answers to 4 questions but is

totally baffled by 6 questions. If the student randomly guesses the answers to

those 6 questions, find a probability density function (pdf) for the number of

correct responses earned. Calculate the mean and standard deviation for t

20. There are 3 urns each containing red and black marbles (see

table below). You draw one marble from Urn 1. If you draw a red marble from Urn

1, you make your second draw from Urn 2. If you draw a black marble from Urn 1,

you make your second draw from Urn 3. What is the probability of drawing two

marbles of the same color? Urn Red Marbles Black Marbles 1 1 9 2 7 3

21. Five number digits are generated in five rounds. In

the first round, a digit from 0, ... , 9 could be selected, with equal

probability. In each further round, if a1...an has already been selected, then

the next number selected could only be n+1, ... , 9 with all these choices

having equal probability. In other words, the digits of the number generated

will always increase, like in 35689 or 24789. Find the probability that a se

(a) terminates after 1, 2, 3 or 4 rounds (e.g. a 9 is selected and, therefore,

the process ends). (b) given a 5-digit is generated, that it consists of all

even integers. (c) consists of all odd integers.

22. In Franklin College, 40% of the freshmen are enrolled in a

mathematics course, and 75% are enrolled in an English course, and 20% are

taking both. (a) What is the probability that a randomly selected freshman is

taking an English course if it is known that he or she is enrolled in a

mathematics course? (b) If a randomly selected freshman is taking an English

course, what is the probability that he or she is also enrolled in a

mathematics course?

23. Eight tennis players (call them A,B,C,D,E,G,F,H) are

randomly assigned to start positions in a ladder tournament. Initially,

position 1 plays position 2, position 3 plays 4, 5 plays 6 and 7 plays 8.

Second round has 2 matches: winner of (1,2) match plays winner of (3,4), and

winner (5,6) plays winner(7,8). The winners of the two 2nd round matches play

each other in the final match. Player A wins against any of the others. Player

B always beats any opponent except player A. What is the probability that

player B wins the 2nd place trophy in the final match?

24. In a roomful of 30 people, what is the probability that at

least two people have the same birthday? Assume birthdays are uniformly

distributed and there is no leap year complication.

25. A coach is training 15 girls. He wants to form 5 lines of 3

forwards each (left-wing, center, and right-wing). Assume that the order of

assigning these positions matters. What is the probability that both Ann and

May are in the same line?

26. What is the probability of receiving a 7 (3 letters, then 4

numbers) digit license plate with a repeated letter/number?

27. What is the probability of having a license plate (3

letters, then 4 numbers) with either all vowels OR consonances?

28. What is the probability of randomly selecting a bill from a

wallet and getting a $20 bill out of a wallet with 2 tens, 3 fives, 4 twenties,

and 7 ones?

29. What is the probability of getting a 70% or better on a 20

question multiple choice test with 4 choices each, randomly guessing?

30. A certain school has three exam slots per day and 4 days for

finals. Assuming exams are scheduled at random, what is the probability of a

student with 5 classes having 3 finals scheduled on a single day?

31. What is the probability of drawing a red or blue marble out

of a bowl with 10 red, 6 blue, 9 green?

32. What is the probability of rolling snake eyes?

33. What is the probability that a five-card poker hand will

contain at least one of each suit?

34. When selecting three cards in an ordered sequence, what is

the probability that the rank of the first card is strictly smaller than the

rank of the second card which, in turn, is strictly smaller than the rank of

the third card?

35. What is the probability of drawing an Ace then a and then

the 3?

36. A die is rolled, find the probability that an even number is

obtained