A bag contains 5 red, 4 green and 3 black balls. If three balls are drawn out…

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A bag contains 5 red, 4 green and 3 black balls. If three balls are drawn out of it at random, what is the probability of drawing exactly 2 red balls ?

  1. A.

    7/22

  2. B.

    10/33

  3. C.

    7/12

  4. D.

    7/11

Attempted by 3 students.

Show answer & explanation

Correct answer: A

Step-by-Step Solution

To calculate the probability of drawing exactly 2 red balls when 3 balls are drawn at random, we use combinations.

  1. Calculate Total Possible Outcomes:

    • Total balls = 5 red + 4 green + 3 black = 12 balls.

    • We need to choose 3 balls out of 12.

    • Total ways = 12C3 = (12 × 11 × 10) / (3 × 2 × 1) = 220.

  2. Calculate Favorable Outcomes:

    • We need exactly 2 red balls and 1 non-red ball.

    • Ways to choose 2 red balls from 5 = 5C2 = (5 × 4) / (2 × 1) = 10.

    • Number of non-red balls = 4 green + 3 black = 7.

    • Ways to choose 1 non-red ball from 7 = 7C1 = 7.

    • Total favorable ways = 10 × 7 = 70.

  3. Calculate Probability:

    • Probability = Favorable outcomes / Total outcomes = 70 / 220.

    • Simplifying by dividing by 10: 7/22.

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