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Previous Year Question (PYQs)

A bag contain different kind of balls in which 5 yellow, 4 black & 3 green balls. If 3 balls are drawn at random then find the probability that no black ball is chosen




Solution

Probability — No Black Ball is Chosen

Given:

  • Yellow balls = 5
  • Black balls = 4
  • Green balls = 3
  • Total balls = 5 + 4 + 3 = 12

We are to find:

Probability that no black ball is selected when 3 balls are drawn at random.

Step 1: Total number of ways to choose any 3 balls from 12:

\[ \text{Total ways} = \binom{12}{3} = 220 \]

Step 2: Ways to choose 3 balls such that no black ball is chosen:

Only yellow and green balls are allowed ⇒ Total = 5 (yellow) + 3 (green) = 8
\[ \text{Favorable ways} = \binom{8}{3} = 56 \]

Step 3: Probability

\[ P(\text{no black ball}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{56}{220} = \frac{14}{55} \]

\[ \boxed{\text{Probability} = \frac{14}{55}} \]


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Sample Account , Other
Commented Jan 28 , 2024
To find the probability that no black ball is chosen when drawing 3 balls at random, we can use the concept of probability. Total number of balls = 5 yellow + 4 black + 3 green = 12 balls Number of ways to choose 3 balls out of 12 = C(12, 3) = 220 (combination formula) Now, let's find the number of ways to choose 3 balls without any black ball: Number of ways to choose 3 balls without black = C(8, 3) * C(4, 0) = C(8, 3) * 1 (Choosing 0 black balls from 4 black balls) = 56 * 1 = 56 So, the probability P(no black ball) = (Number of ways to choose 3 balls without black) / (Total number of ways to choose 3 balls) P(no black ball)= 56/220 Simplify the fraction: P(no black ball)= 14/55 Therefore, the probability that no black ball is chosen when drawing 3 balls at random is 14/55.

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