Multiple choice

A bag contains $5$ red, $6$ white and $7$ black balls. Two balls are drawn at random. What is the probability that both balls are red or both are black?

  1. $\dfrac {31}{153}$
  2. $\dfrac {30}{153}$
  3. $\dfrac {33}{153}$
  4. $\dfrac {32}{153}$
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A Correct answer
Explanation

Total balls = 18. Ways to choose 2 = 18C2 = 153. Ways to choose 2 red = 5C2 = 10. Ways to choose 2 black = 7C2 = 21. Total favorable = 10 + 21 = 31. Probability = 31/153.

AI explanation

The total number of balls in the bag is 5 red plus 6 white plus 7 black, equaling 18 balls. The number of ways to draw 2 balls from 18 is 18C2, which equals 153. The probability of drawing two red balls is 5C2 divided by 153, equaling 10/153, and the probability of drawing two black balls is 7C2 divided by 153, equaling 21/153. By the addition theorem of probability, the combined probability is (10 + 21) / 153, which is 31/153.

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