Question

Whilst shopping, the probability that Caroline buys fruit is 0.4
The probability that Caroline buys a CD is 0.3
Buying fruit and a CD are independent of each other.
Work out the probability that she only buys fruit, only buys a CD, or buys both.

Answer 1

Let event A = Caroline buys fruit, event B = Caroline buys CD, Ac and Bc are complementary events.

Events AB, ABc, AcB and AcBc are jointly exhaustive and disjoint, hence P(AB) + P(ABc) + P(AcB) +P(AcBc) =1.

Events A and B independent, hence Ac and Bc independent too and probability P(AcBc) = P(Ac)*P(Bc) = (1 - P(A))(1-P(B)) = 0.6*0.4 = 0.24.

Required probability P(AB + ABc + AcB ) = P(AB) + P(ABc) + P(AcB) = 1- P(AcBc) = 1 - 0.24 = 0.76.

Answer: Probability that Caroline buys fruit, a CD or both is 0.76.

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Answer 2

Answer:

0.58

Step-by-step explanation: