Multiple choice

A bag contains $3$ white, $3$ black, and $2$ red balls. One by one three balls are drawn without replacing them, then find the probability that the third ball is red.

  1. $ \displaystyle\frac{1}{4}$
  2. $\displaystyle \frac{3}{4}$
  3. $\displaystyle \frac{1}{3}$

  4. None of these
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A Correct answer
Explanation

In sampling without replacement, the probability of any specific ball appearing at any specific position is equal to the initial proportion of that ball in the bag. Total balls = 8. Red balls = 2. Probability = 2/8 = 1/4.

AI explanation

Using the method of treating the target ball as a fixed position, the probability that the third ball drawn is red is simply the initial proportion of red balls. The total number of balls is 8, and there are 2 red balls. Therefore, the required probability is 2 divided by 8, which equals 1/4.

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