Question

A marketing firm tracks data on grocery store visits. In one study, it finds thatthe probability that a shopper buys bread during a visit to the grocery store is0.70, and the probability that a shopper buys cheese is 0.20.Event A = A shopper buys bread.Event B = A shopper buys cheese.A and B are independent events ifA. the probability of buying bread or cheese is 0.14Ο Ο ΟB. the probability of buying bread or cheese is 0.90C. the probability of buying bread and cheese is 0D. the probability of buying bread and cheese is 0.14

Answer 1

For this problem we recall that:

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Therefore,

$P(A\cap B)=P(A)+P(B)-P(A\cup B)$

and we recall that A and B are independent if and only if

$P(A\cap B)=P(A)\cdot P(B)$

We know that P(A)*P(B)=0.7*0.2=0.14. For the variables to be independent: The probability of buying bread and cheese is 0.14.