Final answer:
The probability that the 3 balls drawn consist of 2 red balls and 1 black ball can be found by considering the different combinations of urns from which the balls are drawn. The probabilities of each combination can be calculated and then added up to find the total probability.
Step-by-step explanation:
To find the probability that the 3 balls drawn consist of 2 red balls and 1 black ball, we need to consider the different combinations of urns from which the balls are drawn
Let's calculate the probability of each combination:
1) The probability of drawing a red ball from urn A is 4/7. The probability of drawing a red ball from urn B is 5/9. The probability of drawing a black ball from urn C is 4/8. So the probability of combination 1 occurring is (4/7) * (5/9) * (4/8).
2) The probability of drawing a red ball from urn A is the same as in combination 1. The probability of drawing a black ball from urn B is 4/9. The probability of drawing a red ball from urn C is the same as in combination 1. So the probability of combination 2 occurring is (4/7) * (4/9) * (4/8).
3) The probability of drawing a black ball from urn A is 3/7. The probability of drawing a red ball from urn B is the same as in combination 1. The probability of drawing a red ball from urn C is the same as in combination 1. So the probability of combination 3 occurring is (3/7) * (5/9) * (4/8).
To find the total probability of getting 2 red balls and 1 black ball, we add up the probabilities of each combination:
Total Probability = (4/7) * (5/9) * (4/8) + (4/7) * (4/9) * (4/8) + (3/7) * (5/9) * (4/8)
Simplifying this expression will give us the final answer.