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.
|
|
|
