Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is :

Solution

Maths sir · 2 steps

The card is non-prime, so compare how likely each box makes that, and Box I's share is the answer.

1. Count the primes. Box I (1 to 30) has 10 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Box II (31 to 50) has 5 primes: 31, 37, 41, 43, 47. The number 1 is not prime, so it counts as non-prime.

   Box	P(box)	Non-primes	P(non-prime | box)	Product
   Box I	1/2	30 - 10 = 20	20/30 = 2/3	1/3
   Box II	1/2	20 - 5 = 15	15/20 = 3/4	3/8

   P(I | non-prime) = (1/3)/(1/3 + 3/8) = (8/24)/(17/24) = 8/17

2. So. Box I's share of the total chance of a non-prime card is 8/17, which is option (a).

The idea to keep. In Bayes, multiply each prior by the chance of the observed result, then take your box's share of the total. And remember that 1 is neither prime nor composite.

Answer from the NTA final answer key. Solution by PrepWiser.