SOLUTION: A cell phone salesperson has kept records on the customers who visited the store. 40% of the customers who visited the store were female. Furthermore, the data show that 35% of t

Question 128641: A cell phone salesperson has kept records on the customers who visited the store. 40% of the customers who visited the store were female. Furthermore, the data show that 35% of the females who visited his store purchased a cell phone, while 20% of the males who visited his store purchased a cell phone. Let A1 represent the event that a customer is a female, A 2 represent the event that a customer is a male, and B represent the event that a customer will purchase a phone.
(1) What is the probability that a female customer will purchase a cell phone?
(2) What is the probability that a male customer will purchase a cell phone?
(3) The salesperson has just informed us that a cell phone was purchased. What is the probability that customer was female?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A cell phone salesperson has kept records on the customers who visited the store. 40% of the customers who visited the store were female. Furthermore, the data show that 35% of the females who visited his store purchased a cell phone, while 20% of the males who visited his store purchased a cell phone. Let A1 represent the event that a customer is a female, A 2 represent the event that a customer is a male, and B represent the event that a customer will purchase a phone.
(1) What is the probability that a female customer will purchase a cell phone?
Prob(female AND purchase phone) = P(female)*P(purchase phone|female)
= 0.4*0.35 = 0.14
------------------------------
(2) What is the probability that a male customer will purchase a cell phone?
Prob(male AND purchase phone) = P(male)*P(purchase phone|male)
= 0.6*0.2 = 0.12
-------------------------
(3) The salesperson has just informed us that a cell phone was purchased. What is the probability that customer was female?
P(female|purchased phone)
= P(female AND purchased phone)/P(purchased phone)
= 0.14/[P(purchased phone|female) + P(purchased phone|mle)
= 0.14/[0.14+0.12]
= 0.14/0.26
= 0.5385...
Cheers,
Stan H.

RELATED QUESTIONS
A car dealer has kept records of the customers who visited his showroom. 30% of the... (answered by edjones)

According to a survey only 20% of customers who visited tje website of a major retail... (answered by Boreal)

According to a survey, only 15% of customers who visited the website of a major retail... (answered by Boreal)

According to a survey, only 15% of customers who visited the web site of a major retail... (answered by stanbon)

A random sample of 99 customers, who visited a department store, spent an average of $80... (answered by ewatrrr)

from past records, a store finds that 26% of people who enter the store will make a... (answered by Boreal)

The ratio of number of pupils who visited the museum to the number of pupils who visited... (answered by ikleyn)

Of the 600 people who visited the Amazing Art Museum on Tuesday, 45% were children.... (answered by jim_thompson5910)

A major cell phone service provider has determined that the number of minutes that its... (answered by stanbon)