question:If P(A) = 2/15, P(B) = 4/15, and P(A B) = 11/15 Find P(A|B)
Options:
(A) 11/4
(B) 2/3
(C) 3/2
(D) 4/5
(E) 4/7
answer:(A)
Stream of consciousness:P(A|B) = P(A B)/P(B)
P(A|B) = (11/15)/(4/15) = 11/4.

question:Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
Options:
(A) 5/11
(B) 6/11
(C) 7/11
(D) 8/11
(E) 9/11
answer:(B)
Stream of consciousness:Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11

question:A class consists of 100 students, 25 of them are girls and 75 boys; 20 of them are rich and remaining poor; 10 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
Options:
(A) 1/200
(B) 1/59
(C) 1/56
(D) 1/54
(E) 1/53
answer:
(A)
Stream of consciousness:The probability of selecting girl is: 25/100 = 1/4
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 10/100 = 1/10
Three are independent;probability of rich and fair complexioned girl is:
(1/4) (1/5) (1/10) = 1/200