Question

In a car hire company there are four tourist taxi drivers A, B, C, D who attend to duties. On an
average 20% of the jobs are assigned to A, 60% to B, 15% to C and the remaining 5% to D. Customers
complain against A once in about 20 trips, against B once in about 15 trips, against C once in 10 trips
and against D once in 15 trips. If a complaint is received, what is the probability that A was the driver?​

Answer 1

Given :  In a car hire company there are four tourist taxi drivers A, B, C, D who attend to duties. On an average 20% of the jobs are assigned to A, 60% to B, 15% to C and the remaining 5% to D

To find :  If a complaint is received, what is the probability that A was the driver

Solution:

A  = 20 %

B = 60%

C = 15%

D  = 5 %

Complaint Against A  =  1/20

Complaint Against B  =  1/15

Complaint Against C  =  1/10

Complaint Against D  =  1/15

Chances of A complaint  for Every 100 trip  =  20/20   = 1

Chances of B complaint  for Every 100 trip  =  60/15   = 4

Chances of C complaint  for Every 100 trip  = 15/10   = 3/2

Chances of D complaint  for Every 100 trip  = 5/15   = 1/3

Total Complaint received =  1 + 4 + 3/2  + 1/3

= ( 30 + 9 + 2)/6

= 41/6

probability that A was the driver  for compalint received  =  1/(41/6)

= 6/41

6/41  is the probability that A was Driver

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