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A bag has n balls. The probability that exactly r of them are white is proportional to r² for 0 ≤ r ≤ n. If one ball is selected at random and it turns out to be white, then the probability that all the balls in the bag are white is:
- 2n/(n+1)²
- 4n/(n+1)²
- 2n/(n+3)²
- 4n/(n+3)²
Correct answer: 4n/(n+1)²
Solution
The correct option is right because the probability of selecting a white ball is influenced by the total number of white balls, which follows a quadratic relationship. Given that the probability of exactly r white balls is proportional to r², the calculations lead to the conclusion that the probability of all balls being white, given one is white, simplifies to 4n/(n+1)².
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