A small software company has three customer service representatives. After a week of observation, the supervisor of the customer service department determines that there is an 85% probability that a customer service representative will be on the phone with a customer at any given time. What is the probability of all three representatives being on the phone at the same time? Round to the nearest percent if necessary.
A.

28%

B.

72%

C.

39%

D.

61%

Question

A small software company has three customer service representatives. After a week of observation, the supervisor of the customer service department determines that there is an 85% probability that a customer service representative will be on the phone with a customer at any given time. What is the probability of all three representatives being on the phone at the same time? Round to the nearest percent if necessary.
 A.	
 
28%
 
 B.	
 
72%
 
 C.	
 
39%
 
 D.	
 
61%

nurali · Answer

First,the event is an independent one bcos the occurrence of one does not prevent the occurrence of the others.that is the 3 representatives can be on the phone at the same time. 
If the probability that a customer rep. will be on the phone is 85/100 (that is 17/20) then the probability that the 3 reps will be on the phone is 
(17/20)^3 
=0.85^3 and that is 0.614 and it is equal to 61%.