Question

Angus goes to one of two coffee shops in his home town. He goes to Tarbucks 67 % of the time and otherwise goes to Costly Coffee. Either way, he buys a latte 60 % of the time, regardless of which place he chose.

a. You are told that Angus went into town for a coffee today. What is the probability (to 3 decimal places) that he had a latte at Tarbucks?
b. Define two events as follows:
L = Angus had a latte
T = Angus went to Tarbucks
Are the two events independent?

1. Yes
2. No

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

Answer 1

Answer:

Detailed step wise solution is given below:

Answer 2

Probabilities are used to determine the chances of an event.

• The probability that the had a latte at Tarbucks is 0.402
• The events are independent
• The probability that he drank at costly fee is 0.198
• The probability that the went to Tarbucks or had a latte or both is 0.370

The given parameters are:

$\mathbf{P(T) = 67\%}$

$\mathbf{P(L) = 60\%}$

$\mathbf{P(C) = 1 - P(T) = 33\%}$

(a) The probability that the had a latte at Tarbucks

This is calculated as:

$\mathbf{Pr = P(T) \times P(L)}$

So, we have:

$\mathbf{Pr = 67\% \times 60\%}$

$\mathbf{Pr = 0.402}$

The probability that the had a latte at Tarbucks is 0.402

(b) Are L and T independent

The events are independent, because whether he goes to Tarbucks or not, he will have a latte, 60% of the times

(c) Given that he had latte, the probability that he drank at costly fee

This is calculated as:

$\mathbf{Pr = P(C ) \times P(L)}}$

$\mathbf{Pr = 33\% \times 60\%}$

$\mathbf{Pr = 0.198}$

The probability that he drank at costly fee is 0.198

(d) The probability that the went to Tarbucks or had a latte or both

This is calculated as:

$\mathbf{Pr = P(T) + P(L) - P(T) \times P(L)}$

$\mathbf{Pr = 67\% + 60\% - 0.402}$

$\mathbf{Pr = 0.370}$

The probability that the went to Tarbucks or had a latte or both is 0.370

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