Multiple choice

A bag contains $8$ red and $7$ black balls. Two baIls are drawn at random. The probability that both the baIls are ofthe same colour is

  1. $\displaystyle \frac{14}{15}$
  2. $\displaystyle \frac{11}{15}$
  3. $\displaystyle \frac{7}{15}$
  4. $\displaystyle \frac{4}{15}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total balls = 15. Ways to pick 2 balls = 15C2 = 105. Ways to pick 2 red = 8C2 = 28. Ways to pick 2 black = 7C2 = 21. Total favorable ways = 28 + 21 = 49. Probability = 49/105 = 7/15.

AI explanation

The total ways to draw 2 balls from 15 is given by the combination 15C2, which equals 105. The favourable outcomes are drawing 2 red balls from 8, which is 8C2 equalling 28, or 2 black balls from 7, which is 7C2 equalling 21. The probability is the sum of these favourable events divided by the total outcomes, which is (28 plus 21) divided by 105, simplifying to 7/15.

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