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5 votes
There are 6

black balls and 9
red balls in an urn. If 3
balls are drawn without replacement, what is the probability that exactly 1
black ball is drawn? Express your answer as a fraction or a decimal number rounded to four decimal places.

User Vityata
by
8.7k points

1 Answer

5 votes

Answer: To find the probability of exactly 1 black ball being drawn when 3 balls are drawn without replacement, we can use the concept of combinations.

Total number of balls in the urn = 6 black balls + 9 red balls = 15 balls

We want to find the probability of drawing 1 black ball and 2 red balls.

Step 1: Find the number of ways to choose 1 black ball from 6 black balls:

Number of ways to choose 1 black ball = C(6, 1) = 6

Step 2: Find the number of ways to choose 2 red balls from 9 red balls:

Number of ways to choose 2 red balls = C(9, 2) = 36

Step 3: Find the total number of ways to choose 3 balls from 15 balls:

Total number of ways to choose 3 balls = C(15, 3) = 455

Step 4: Find the probability of exactly 1 black ball being drawn:

Probability = (Number of ways to choose 1 black ball * Number of ways to choose 2 red balls) / Total number of ways to choose 3 balls

Probability = (6 * 36) / 455

Probability ≈ 0.4775 (rounded to four decimal places)

So, the probability of exactly 1 black ball being drawn is approximately 0.4775 or 47.75%.

User Bhanu Sinha
by
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