Answer to Question #309517 in Statistics and Probability for caroline

Question

Each time Caroline goes shopping she decides whether or not to buy fruit.

The probability that she does buy fruit is 0.6.

Independently, she then decides whether or not to buy a CD, with a probability of 0.2 that she does buy a CD.

Work out the probability that she buys fruit or buys a CD or both.

Answer 1

Probability of buying fruit, $P(f)=0.6$

Probability of buying a CD, $P(CD)=0.2$

Since Independent, $P(f and CD)=P(f)*P(CD)$

$=0.6*0.2=0.12$

Probability of buying fruit, a CD, or both is $P(f)+P(CD)-P(fandCD)$

$=0.6+0.2-0.12$

$=0.68$