An automobile dealer has kept records on the customers who visited his showroom. Forty percent of the people who visited his dealership were women. Furthermore, his records show that 37% of the women who visited his dealership purchased an automobile, while 21% of the men who visited his dealership purchased an automobile.
a. What is the probability that a customer entering the showroom will buy an automobile?
b. Suppose a customer visited the showroom and purchased a car. What is the probability that the customer was a woman?
c​. ​Suppose a customer visited the showroom but did not purchase a car. What is the probability that the customer was a man?

Respuesta :

Answer:

Step-by-step explanation:

(let's assume that people are either classified as man or woman)

m=man

b=buy

a

a.) we are looking for b

we are given

m'=.4

b|m'=.37

b|m=.21

b=b∩m+b∩m'

b∩m= (1-.4)(.21)

b∩m'=.4*.37

b= .274

b.) we are looking for m'|b

m'|b= m'∩b/b

m'∩b=.4*.37

b= .274

m'|b=.540145985

c.)

m|b'= m∩b'/b'

m=m∩b'+m∩b (law of total probability)

.6=m∩b'+.6*.21

m∩b'=.474

.474/(1-.274)= .652892561985

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