CHAPTER 5

EXERCISES.

1. A balanced (fair) die is tossed once. Determine the probability of each of the following events:

a.)Obtaining at least a 2

b.)Obtaining at most a 3

c.)Obtaining more than 4

d.)Obtaining 5 or less

e.)Obtaining a 3 or more

f.)Obtaining less than 6

g.)Obtaining at least 3 but less than 5

h.)Obtaining more than 2 and 5 or less

2. An urn contains three white, two red, one blue and four black balls. If one ball is drawn at random, what is the probability that it is:

a.) Black

b.) either Black or White

c.) not White

d.) both White and Blue

e.) either Black or Blue

3. Which of the following are examples of independent events?

a.) Obtaining a three and a four in one roll of two fair dice

b.) Obtaining an ace and a king in that order by drawing twice without replacement of a deck of

cards

c.) Obtaining an ace and a king in that order by drawing twice with replacement from a deck of

cards

d.) A cloudy sky followed by train

e.) A full moon and eating a hamburger

4.) Which of the following are examples of mutually exclusive events?

a.) Obtaining a four and a seven in one draw from a deck of ordinary playing cards

b.) Obtaining a three and a four in one roll of two fair dice

c.) Being male and becoming pregnant

d.) Obtaining a one and an even number in one roll of a dice

e.) Getting married and becoming a bachelor

5. If you are randomly sampling one at a time with replacement from a bag that contains eight blue marble, seven red marbles, what is the probability of obtaining

a.) A blue marble in one draw from the bag?

b.) Three blue marbles in three draws from the bag?

c.) A red, a green, and a blue marble in that order in three draws from the bag?

d.) At least two red marbles in three draws from the bag?

6. If you are randomly sampling one at a time without replacement from a bag that contains eight blue marbles, seven red marbles and five green marbles, what is the probability of obtaining

a.) A blue marble in one draw from a bag?

b.) three blue marbles in three draws from a bag?

c.) A red, a green and a blue marble in that order in three draws from the bag?

d.) At least two red marbles in three draws from the bag?

7. You want to call a friend on the telephone. You remember the first three digits of her phone number, but you have forgotten the last four digits. What is the probability that you will get the correct number merely by guessing?

1.You are planning to make a "killing" at the racetrack. In a particular race, there are seven horses entered. If the horses are equally matched, what is the probability of you correctly picking the winner and the runner-up?

2.Given a population composed of 30 bats, 15 gloves and 60 balls if sampling is random and one at time without replacement,

a.)What is the probability of obtaining a glove if one object sampled from the population?

b.)What is the probability of obtaining a bat and a ball if two objects are sampled from the population?

c.)What is the probability of obtaining a bat, a glove and a bat in that order if three objects are sampled from the population?

3.In a game of chance, two integers are randomly selected from 1 to 10 inclusive, the same under may be selected twice. If both numbers agree, then the person wins the game. Find the exact probability of winning this game.

Consul de Guzman, on of the judges at a car show, counts the different cars by brand and also notes whether the owner is a woman or a man. Some of the results are shown here

Sex of owner Nissan Toyota Civic Mercedes

Male 12 34 21 36

Female 9 43 36 14

What is the probability that:

a.)The owner is female, given that the car is a Mercedes?

b.)The car is a Nissan, given that the owner is male?

c.)The owner male, given that the car is a Nissan?

12. Find the P (A and B) if P (A) = , P(B) = 1/3 and:

a.)P(A or B) = 4/5

b.)P(A/B) =

c.)P(B/A) = 2/5

d.)A and B are independent

e.)A and B are mutually exclusive

13. Find the P(A/B) if P (A) = 2/3, P(B) = 1/5 and :

a.) P(A/B) = 0.1

b.) P(B/A) = 0.1

c.) P(A/B) = P(A)

d.) P(B/A) = P(B)

14. Among the 200 inmates of a prison, some are first offenders, others are second offenders, still other are serving longer sentences. The exact breakdown is

Sentences less : Longer

than 2 years : sentences

First offenders:60 :20

Second offenders:40 :80

15. If one of the inmates is to be selected at random to be released, S is the event that he is second time offender, and L is the event that he is serving a longer sentence, determine each of the following probabilities directly from the entries of the row and column totals of the table:

a)P (S)d)P (S' L)

b)P (L)e)P (L/S)

c)P (L S)f)P (S' /L)