Multiple choice

Two balls are drawn from a bag containing $5$ white and $7$ black balls at random. What is the probability that they would be of different colours?

  1. $\dfrac{35}{66}$
  2. $\dfrac{30}{66}$
  3. $\dfrac{12}{66}$

  4. None of above
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A Correct answer
Explanation

Total balls = 12. Selecting 2 balls: 12C2 = 66. Different colors means 1 white and 1 black: 5C1 * 7C1 = 35. Probability = 35/66.

AI explanation

Using the combinations method for probability, the total number of ways to draw 2 balls from 12 is 12C2, which equals 66. The number of favorable ways to draw one ball of each color is the product of choosing 1 white ball out of 5 and 1 black ball out of 7, written as 5C1 multiplied by 7C1, giving 35. The probability is the ratio of favorable outcomes to total outcomes, calculated as 35 divided by 66. The result is 35/66.

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