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

Question

Aicharya · Accepted Answer

P B 1 = 1 2 = P B 2 Box B 1 have 20 non-prime numbers 1 , &#160; 4 , &#160; 6 , &#160; 8 , &#160; 9 , &#160; 10 , &#160; 12 , &#160; 14 , &#160; 15 , &#160; 16 , &#160; 18 , &#160; 20 , &#160; 21 , &#160; 22 , &#160; 24 , &#160; 25 , &#160; 26 , &#160; 27 , &#160; 28 , &#160; 30 &#8658; P N P / B 1 = 20 30 Box B 1 have 15 non-prime numbers 32 , &#160; 33 , &#160; 34 , &#160; 35 , &#160; 36 , &#160; 38 , &#160; 39 , &#160; 40 , &#160; 42 , &#160; 44 , &#160; 45 , &#160; 46 , &#160; 48 , &#160; 49 , &#160; 50 &#8658; 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 &#183; 20 30 + 1 2 &#183; 15 20 P B 1 / N P = 1 2 &#183; 20 30 1 2 &#183; 20 30 + 1 2 &#183; 15 20 = 8 17

Box 1 contains 30 cards numbered 1 to 30 and Box 2 contains 20 cards numbered 31 to 50 . A box is selected…

Solution