Question

At a store, the probability that a customer buys socks is 0.15. The probability

that a customer buys socks given that the customer buys shoes is 0.20.
Which statement is true?
O
A. Buying socks and buying shoes are dependent events.
O
B. The probability that a customer buys socks and shoes is 0.05.
C. Every customer who buys shoes also buys socks.
D. Buying socks and buying shoes are independent events.

Answer 1

A. Buying socks and buying shoes are dependent events.

Explanation:

We are given that

The probability that a customer buys socks ,P(A)=0.15

The probability that a customer socks given that the customer buys shoes P(A\B)=0.20

The probability that a customer buys shoes,P(B)=1-0.15=0.85

By using formula P(E')=1-P(E)

Where P(E)= Probability of an event that is happened

P(E')=Probability of an event that is not happened

We have to find
`P(A\capB)` for two events

`P(A)\cdot P(B)`

`=0.85* 0.15=0.1275`

We know that conditional probability of an event when given that the probability of an event B is given

`P((A)/(B))=(P(A\cap B))/(P(B))`

`0.20=(P(A\cap B))/(0.85)`

`P(A\cap B)=0.20* 0.85=0.17`

`P(A\cap B)\\eq P(A)\cdot P(B)`.

Therefore, the two events are dependent .Hence, Buying socks and buying shoes are dependent events.

Therefore, option A is true.