# Box I contains 30 cards numbered I to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random

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Box I contains 30 cards numbered I 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 :

(1) $2\over3$

(2) $2\over5$

(3) $8\over17$

(4) $4\over17$

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Ans. (3) $8\over17$

Sol. $P(B_1) = {1\over2} = P(B_2)$

P(Non-prime) = P(B1). P(N.P/B1) + P(B2). P(N.P/B2)

$={1\over2}.{20\over30}+{1\over2}.{15\over20}$

P(B1/N.P) $={{1\over2}.{20\over30}\over{1\over2}.{20\over30}+{1\over2}.{15\over20}}={8\over17}$

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This solution of Probability chapter is probably good.