Suppose that of all individuals buying a certain digital camera, 60% include a m

Question

Suppose that of all individuals buying a certain digital camera, 60% include a memory card in their purchase, 40% include an extra battery in their purchase and 30% include both a card and an extra battery. Define the events A = {memory card purchased} and B = {extra battery purchased). If a buyer is selected at random Given that the selected individual purchased an extra battery what is the probability that he also purchased a memory card? Are the events A and B independent? Explain your answer.

Explanation / Answer

A= memory card purchased

B = extra battety purchased

P(A) = 0.60

P(B) = 0.40

P(AB) = 0.30

(a) P(A/B):

By multiplication theorem,

P(A/B) P(B) = P(AB)

So,

P(A/B) = P(AB)/P(B)

           = 0.30/0.40 = 0.75

(b) Events A and B are independent:

If P(A/B) = P(A)

Here,

P(A/B) = 0.75

P(A) = 0.60

So, A and B are not independent.

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