+598 Market research for an online electronics retailer showed that 23% of its customers purchased a smart phone. 12% of these smartphone customers used an online payment system (such as Paypal) to pay for their purchases, i.e., given that a customer purchased a smart phone, the probability was 12% that he/she used an online payment system to pay. In general, 8% of the customers used an online payment system to pay for their purchases. (10 Points)
a. What percent of customers did not purchase a smart phone?
100 - 23 = 77 Therefore, 77% of customers did not purchase a smart phone.
b. What percent of customers purchased a smart phone and used an online payment system to pay?
12% . It states this information above in the question.
c. What percent of customers purchased a smart phone or used an online payment system to pay?
d. Are the events “purchased a smart phone” and “used an online payment system to pay” mutually exclusive? Why or why not.
e. Are the events “purchased a smart phone” and “used an online payment system to pay” independent? Use probabilities to justify your answer.
I have answered the first two questions - which I believe my answers to be correct. I am struggling with the other 3. Any help would be greatly appreciated, with calculations - Thanks.
+129850 I believe that (b) should be this......
23% of the customers purchased a smartphone....of these, 12% paid online......so
The % of total customers that purchased a smartphone AND paid online =
12% of 23% = .12 * .23 = about 2.76% of the total customers
(c) Let A be the probability that a customer purchased a smartphone = .23
Let B be the probability that a customer paid on line = ..08
Let P(A and B) = .0276
So
P( A or B) = P(A) + P(B) - P(A and B) =
.23 + .08 - .0276 =
.2824 =
about 28.24% of the total customers purchased a smartphone or paid online
(d) The events buying a smartphone and paying online aren't mutually exclusive, brcause we could have purchased a smartphone and paid online
(e) If P(A and B) = P(A) * P(B) .....then the events are independent
So
P(A and B) = .0276
P(A) = .23
P(B) = .08
But
.0276 = .23 * .08 ???
.0276 = .0184
So.....these events are not independent
+598 Thanks for all your help Phil. I have posted one more in the forum if you want to give it a shot. It will also be my final one.
Thanks again
