Multiple choice

An urn contains $7$ white, $5$ black and $3$ red balls. Two are drawn at random. Find the probability that Both the balls are red.

  1. $\dfrac {34}{35}$
  2. $\dfrac {1}{35}$
  3. $\dfrac {1}{7}$
  4. $\dfrac {1}{5}$
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B Correct answer
Explanation

Total balls = 7+5+3 = 15. Probability of first red = 3/15 = 1/5. Probability of second red = 2/14 = 1/7. Total = 1/5 * 1/7 = 1/35.

AI explanation

The total number of balls in the urn is 7 white plus 5 black plus 3 red, giving 15 balls. The total number of ways to draw 2 balls from 15 is 15C2, which equals 105. The number of favorable ways to draw 2 red balls from the 3 available is 3C2, which equals 3. The required probability is 3/105, which simplifies to 1/35.

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