Probability (Class 12) · Question 17

Given three identical bags each containing 10 balls, whose colours are as follows : arraylccc & Red & Blue & Green \ Bag I & 3 & 2 & 5 \ Bag II & 4 & 3 & 3 \ Bag III & 5 & 1 & 4 array A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the ball is Green, the probability that it is from bag III is q, then the value of ( 1p + 1q ) is:

1. 6
2. 9
3. 7
4. 8

Answer

(3) 7

Solution

Each bag is chosen with probability 13.

Red ball:

P(R) = 13 ( 310 + 410 + 510 ) = 1230

By Bayes' theorem, p = P(I R) = 13 310 1230 = 312 = 14

Green ball:

P(G) = 13 ( 510 + 310 + 410 ) = 1230

q = P(III G) = 13 410 1230 = 412 = 13

1p + 1q = 4 + 3 = 7

Answer: (3)