Multiple choice

A box contains 4 black and 5 red balls and another box contains 5 black and 4 red balls. One ball is to drawn from either of two boxes. What is the probability of drawing a black ball?

  1. 1/2

  2. 3/2

  3. 2/3

  4. 5/2

  5. 2/5
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A Correct answer
Explanation

First box: 4 black, 5 red balls (total 9). Probability of black from box 1 = 4/9. Second box: 5 black, 4 red balls (total 9). Probability of black from box 2 = 5/9. Since one box is chosen at random (probability 1/2 for each box), total probability of black ball = (1/2)(4/9) + (1/2)(5/9) = 2/9 + 2.5/9 = 4.5/9 = 1/2.

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