Multiple choice

A bag contains 7 red pens and 5 blue pens and another bag contains 4 red pens and 8 blue pens. One bag is chosen randomly and one pen is drawn from it. If the pen drawn is red, then what is the probability that it is from the first bag?

  1. 7/22

  2. 11/18

  3. 7/11

  4. 17/24

  5. 8/17
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C Correct answer
Explanation

Using Bayes' Theorem: P(Bag1|Red) = P(Red|Bag1)P(Bag1) / (P(Red|Bag1)P(Bag1) + P(Red|Bag2)P(Bag2)). P(Red|Bag1) = 7/12, P(Red|Bag2) = 4/12. P(Bag1) = P(Bag2) = 1/2. Calculation: (7/12 * 1/2) / ((7/12 * 1/2) + (4/12 * 1/2)) = 7/11.

AI explanation

Using Bayes' theorem, we find the probability that the red pen came from the first bag. The prior probability of choosing either bag is 1/2. The probability of drawing a red pen from the first bag is 7/12, and from the second bag is 4/12. The calculation is (1/2 * 7/12) divided by the total probability of drawing a red pen, which is (1/2 * 7/12 + 1/2 * 4/12). This gives (7/24) divided by (11/24), resulting in a probability of 7/11.

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