Box 1 contains 30 cards numbered 1 to 30 and Box 2 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 numb

Question

Box 1 contains 30 cards numbered 1 to 30 and Box 2 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 1 is

TestHub · Accepted Answer

P B 1 = 1 2 = P B 2 Box B 1 have 20 non-prime numbers 1 , 4 , 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 18 , 20 , 21 , 22 , 24 , 25 , 26 , 27 , 28 , 30 ⇒ P N P / B 1 = 20 30 Box B 1 have 15 non-prime numbers 32 , 33 , 34 , 35 , 36 , 38 , 39 , 40 , 42 , 44 , 45 , 46 , 48 , 49 , 50 ⇒ P N P / B 2 = 15 20 Probability of non-prime = P N P . P N P = P B 1 . P N P / B 1 + P B 2 . P N P / B 2 = 1 2 · 20 30 + 1 2 · 15 20 P B 1 / N P = 1 2 · 20 30 1 2 · 20 30 + 1 2 · 15 20 = 8 17

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