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For each k = 1, 2, 3, the box Bₖ has k red balls and (k + 1) white balls. The probabilities of choosing B₁, B₂ and B₃ are 1/2, 1/3 and 1/6 respectively. One box is picked at random and then one ball is taken out. Given that the ball drawn is red, what is the probability that it was drawn from B₂?
- 35/78
- 14/39
- 10/13
- 12/13
Correct answer: 14/39
Solution
The probability of drawing a red ball from box B₂, given that a red ball was drawn, is calculated using Bayes' theorem. By considering the total probability of drawing a red ball from all boxes and the specific probability from B₂, we find that the correct probability is 14/39.
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