# Statistique Random Variable

2006 – 2007

Exercises

(Probability and Random Variables)

Exercise 1

Suppose that we have a sample space with five equally likely experimental outcomes : E1,E2,E3,E4,E5.

Let

A = {E1,E2}

B = {E3,E4}

C = {E2,E3,E5}

a. Find P(A), P(B), P(C).

b. Find P(A U B) . Are A and B mutually exclusive?

c. Find Ac, Bc, P(Ac), P(Bc).

d. Find A U Bc and P(A U Bc)

e. Find P(B U C)

Exercise 2

A committee with two members is to be selected from a collection of 30 people, of whom 10 are males and 20 are females.

a. Find the probability that both members are male

b. Find the probability that both members are female

c. Find the probability that one member is male and one is female.

Exercise 3

A warehouse contains 100 tires, of which 5 are defective.

Four tires are chosen at random for a new car.

Find the probability that all four are good.

Exercise 4

In a particular city,

40% of the people subscribe to magazine A, 30% of the people subscribe to magazine B and 50% to magazine C.

However, 10% subscribe to both A and B, 25% subscribe to both A and C, 15% subscribe to both B and C. Finally, 5% subscribe to all three magazines.

A person is chosen at random.

a. What is the probability that the chosen person subscribes to at least one magazine? b. What is the probability that the chosen person subscribes to at least two magazines? c. Find the conditional probability that a person subscribes to magazine A given that he or she subscribes to magazine B.

Exercise 5

Let us consider a student who is taking two tests on a given day. Let A be the event that the student passes the first test and B be the event that he passes the second.

Suppose that :

P(A) = 0.6

P(B) = 0.8

P(A ∩ B) = 0.5

a. Find the probability that the student passes the second test given that he passes the first b. Find the probability that the student passes the first test given that he passes the second

Exercise 6

The following table shows...

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