Question

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 draw from Box I is :

(1) 8/17

(2)  2/3

(3) 4/17

(4)  2/5

Answer 1

Answer is (1) 8/17

Let B₁ be the event where Box–I is selected. & B₂ → where box-II selected

P(B₁) = P(B₂) = 1/2

Let E be the event where selected card is non prime.

For B₁ : Prime numbers :

{2, 3, 5, 7, 11, 13, 17, 19, 23, 29}

For B₂ : Prime numbers : 

{31, 37, 41, 43, 47}