Multiple choice

A box contains 3 yellow balls and 5 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?

  1. 1/4

  2. 1/2

  3. 5/8

  4. 2/3

  5. 3/4
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C Correct answer
Explanation

In a random selection without replacement, the probability that the k-th item is of a certain type is the same as the probability that the first item is of that type. Probability = 5 / (3 + 5) = 5/8.

AI explanation

By the principle of symmetry, drawing without replacement means any of the 8 balls is equally likely to be in the fourth position. The total number of balls is 8, and the number of black balls is 5. The probability that the fourth ball selected is black is therefore 5 divided by 8.

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