Multiple choice

A box contains 3 white and 2 black balls. Two balls are drawn at random one after the other. If the balls are not replaced, what is the probability that both the balls are black?

  1. 2/5

  2. 1/5

  3. 1/10

  4. None of the above

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total balls = 5. Probability of first black = 2/5. Probability of second black (without replacement) = 1/4. Total probability = (2/5) * (1/4) = 2/20 = 1/10.

AI explanation

The probability of drawing a black ball on the first draw is the number of black balls divided by the total balls, which is 2/5. Since the ball is not replaced, there is now 1 black ball left out of 4 total balls, making the probability of drawing a black ball on the second draw 1/4. According to the multiplication theorem for dependent events, the combined probability is the product of the two probabilities: 2/5 times 1/4 equals 2/20, which simplifies to 1/10. The probability that both balls are black is 1/10.