Multiple choice

A bag contains 4 tickets numbered 1, 2, 3, 4 and another bag contains 6 tickets numbered 2, 4, 6, 7, 8, 9. One bag is chosen and a ticket is drawn. The probability that the ticket bears the number 4, is equal to

  1. 5/12

  2. 5/24

  3. 7/12

  4. 19/24
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B Correct answer
Explanation

Probability of choosing a bag is 1/2. In bag 1 (1, 2, 3, 4), P(4) = 1/4. In bag 2 (2, 4, 6, 7, 8, 9), P(4) = 1/6. Total probability = (1/2 * 1/4) + (1/2 * 1/6) = 1/8 + 1/12 = 3/24 + 2/24 = 5/24.

AI explanation

Using the law of total probability, the chance of selecting either bag is 1/2. Drawing a 4 from the first bag has a probability of 1/4, while drawing a 4 from the second bag has a probability of 1/6. The overall probability is (1/2 multiplied by 1/4) plus (1/2 multiplied by 1/6), which equals 1/8 plus 1/12, resulting in 5/24.

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