Multiple choice

An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?

  1. 3/7

  2. 7/3

  3. 1/7

  4. 1/3
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A Correct answer
Explanation

There are 15 balls total. The probability of drawing the first black ball is 10/15 = 2/3. After drawing one black ball, 9 black balls and 14 total balls remain, so the probability of the second being black is 9/14. The total probability is (2/3) * (9/14) = 18/42 = 3/7.

AI explanation

Using the multiplication theorem for dependent events, the required probability is the product of the probabilities of drawing a black ball each time. The probability of drawing a black ball first is 10 out of 15, which is 2/3. Since the ball is not replaced, the probability of drawing a second black ball is 9 out of 14, making the final calculation (2/3) * (9/14), which equals 3/7.

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