Angus goes to one of two coffee shops in his home town. He goes to Tarbucks 70 %

Question

Angus goes to one of two coffee shops in his home town. He goes to Tarbucks 70 % of the time and otherwise goes to Costly Coffee. Either way, he buys a latte 68 % of the time, regardless of which place he chose.

Part a)
You are told that Angus went into town for a coffee today. What is the probability (to 3 d.p.) that he had a latte at Tarbucks?


Part b)
Define two events as follows:
L = Angus had a latte
T = Angus went to Tarbucks
Are the two events independent?

A. No
B. Yes


Part c)
Given that Angus had a latte in town, what is the probability (to 3 d.p.) that he drank at Costly Coffee?


Part d)
What is the probability (to 3 d.p.) that Angus went to Tarbucks or had a latte or both?

Explanation / Answer

Let

T = tarbucks
C= costly coffee
L = latte

a)

P(L n T) = P(T) P(L|T) = 0.70*0.68 = 0.476 [ANSWER]

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b)

A: YES.

This is because he buys a latte 68% of the time regardless of coffee house.

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c)

As drinking latte is independent of coffe house, then

P(C|L) = P(C) = 0.30 [ANSWER]

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d)

P(T U L) = P(T) + P(L) - P(T) P(L|T)

= 0.70 + 0.68 - 0.70*0.68

= 0.904 [ANSWER]

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