Multiple choice

A bag contains 10 white and 15 black balls. Two balls are drawn without replacement find the probability that first is black and second is white......

  1. $\dfrac{1}{7}$
  2. $\dfrac{1}{4}$
  3. $\dfrac{1}{8}$
  4. $\dfrac{1}{5}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total balls = 25. P(first is black) = 15/25 = 3/5. After removing one black ball, 24 balls remain (10 white, 14 black). P(second is white | first is black) = 10/24 = 5/12. Probability = (3/5) * (5/12) = 15/60 = 1/4.

AI explanation

Using the multiplication theorem for dependent events, the required probability is the product of the probability of the first ball being black and the probability of the second ball being white given the first was black. The total balls are 25, so the probability of drawing a black ball first is 15 divided by 25, or 3 divided by 5. Without replacement, 24 balls remain, making the probability of drawing a white ball second 10 divided by 24, or 5 divided by 12. Multiplying these gives 3/5 times 5/12, which simplifies to 1/4.

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