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 :

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Answer: A. {8 \over {17}} Let B1 be the event where Box-I is selected. And B2 be the event where Box-II is selected. P(B1) = P(B2) = {1 \over 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} P(E) = P(B1) 	imes P\left( {{E \over {{B_1}}}} ight) + P(B2) 	imes P\left( {{E \over {{B_2}}}} ight) = {1 \over 2} 	imes {{20} \over {30}} + {1 \over 2} 	imes {{15} \over {20}} Required probability : P\left( {{{{B_1}} \over E}} ight) = {{P\left( {{B_2}} ight).P\left( {{E \over {{B_1}}}} ight)} \over {P\left( E ight)}} = {{{1 \over 2} 	imes {{20} \over {30}}} \over {{1 \over 2} 	imes {{20} \over {30}} + {1 \over 2}{{15} \over {20}}}} = {{{2 \over 3}} \over {{2 \over 3} + {3 \over 4}}} = {8 \over {17}}

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 :

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