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%.