1.-You have a fair fivesided die. The sides of the die are numbered from 1 to 5.

Question

1.-You have a fair fivesided die. The sides of the die are numbered from 1 to 5. Each die roll is independent of all others, and all faces are equally likely to come out on top when the die is rolled. Suppose you roll the die twice. Consider the following events:  

A:  the total of two rolls is 10

B: at least one roll resulted in 5

C: at least one roll resulted in 1

(a) Calculate P[A], P[B], P[C].  

(b) Is event A independent of event B?  

(c) Is event A independent of event C?

2.-Suppose that of all of the customers at a coffee shop: 80% purchase a cup of coffee; 20% purchase a cookie; 10% purchase both a cup of coffee and a cookie.  

(a) What is the probability that a random customer will purchase either a cup of coffee or a cookie?

(b) Given that a randomly chosen customer has purchased a cup of coffee, what is the probability that he/she has also purchased a cookie?

Explanation / Answer

2.

Let C shows the event that cutomer purchase a cup of coffee and O shows the event that cutomer purchase a cookie. So we have following probabilties:

P(C) = 0.80, P(O) = 0.20 and P(C and O) = 0.10

(a)

The probability that a random customer will purchase either a cup of coffee or a cookie is

P(C or O) = P(C) + P(O) - P(C and O) = 0.80+0.20-0.10=0.90

(b)

the probability that cutomer has also purchased a cookie given that he/she  purchased a cup of coffee is

P(O |C) = P( O and C) / P(C) = 0.10/0.80 = 0.125

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