Question

A marketing firm tracks data on grocery store visits. In one study, it finds that the probability that a shopper buys bread during a visit to the grocery store is 0.60, and the probability that a shopper buys cheese is 0.25. Event A A shopper buys bread. Event B- A shopper buys cheese. A and B are independent events if____.

Answer 1

Answer: A and B are independent events if P(A∩B)=P(A).P(B)=0.15.

Explanation:

Let A be the event that a shopper buys bread.

Let B be the event that a shopper buys cheese.

So, P(A∪B)=100

Probability that a shopper buys bread during a visit to the grocery store =n 0.60

P(A) = 0.60

Similarly, Probability that a shopper buys bread = 0.25

P(B) = 0.25

Since A and B are independent then,

`P(A\cap B)=P(A).P(B)=0.60* 0.25=0.15`

So, A and B are independent events if P(A∩B)=P(A).P(B)=0.15.