Question

Two percent of the customers of a store buy cigars. Half of the customers who buy cigars buy beer. 25 percent who buy beer buy cigars. Determine the probability that a customer neither buys beer nor buys cigars. 8) _______

A) 0.96 B) 0.98 C) 0.75 D) 0.95 E) 0.50

Answer 1

Consider A and B be two events that customers of a store buy cigars and beer, respectively.

According to the mentioned data, the probability of customer buying cigars, P(A) is 0.02, the probability of customers who buy cigars buy beer, P(B∣A) is 0.50 and the probability of customers who buy beer buy cigars, P(A∣B) is 0.25.

Therefore, the probability that a customer buys both cigar and beer can be calculated as:

P(A∩B)=P(B∣A)P(A)

=0.50×0.02=0.01

P(A∩B)=P(A∣B)P(B)

P(B)=P(A∩B)/P(A|B)=0.01/0.25=0.04