Answer:
Decimal places
Explanation:
To find the probability of exactly 2 black balls being drawn out of 4 balls without replacement, we need to calculate the probability of selecting 2 black balls and 2 non-black balls.
The total number of balls in the urn is 5 black balls + 7 red balls = 12 balls.
First, let's calculate the probability of selecting 2 black balls out of the 5 black balls in the urn.
The probability of the first ball being black is 5/12.
After selecting a black ball, there are 4 black balls remaining out of 11 total balls.
Therefore, the probability of selecting a second black ball is 4/11.
Next, we need to calculate the probability of selecting 2 non-black balls out of the remaining 7 red balls in the urn.
The probability of the first ball being red is 7/10.
After selecting a red ball, there are 6 red balls remaining out of 9 total balls.
Therefore, the probability of selecting a second red ball is 6/9.
To find the probability of both events happening together (2 black balls and 2 red balls), we multiply the individual probabilities:
(5/12) * (4/11) * (7/10) * (6/9) ≈ 0.0578
Rounded to four decimal places, the probability that exactly 2 black balls are drawn is approximately 0.0578.