Final answer:
a. The probability of selecting 2 red balls is 3/10. b. The probability of selecting 1 red and 1 white ball is 3/5. c. The probability of not selecting any red balls is 2/5. d. The probability of drawing at least one white ball is 3/5.
Step-by-step explanation:
To calculate the probabilities, we need to consider the total number of balls in each box and the number of red balls in each box. Let's calculate the probabilities step by step:
a. Probability of selecting 2 red balls:
In box A, there are 3 red balls and 2 white balls. So, the probability of selecting a red ball on the first draw is 3/5. After removing one red ball, there are 2 red balls and 2 white balls left in the box. So, the probability of selecting another red ball on the second draw is 2/4. Hence, the probability of selecting 2 red balls is (3/5) * (2/4) = 6/20 = 3/10.
b. Probability of selecting 1 red and 1 white ball:
In box A, there are 3 red balls and 2 white balls. So, the probability of selecting a red ball on the first draw is 3/5. After removing one red ball, there are 2 red balls and 2 white balls left in the box. So, the probability of selecting a white ball on the second draw is 2/4. However, we also need to consider the case when we select a white ball on the first draw and a red ball on the second draw. The probability of selecting a white ball on the first draw is 2/5. After removing one white ball, there are 3 red balls and 2 white balls left in the box. So, the probability of selecting a red ball on the second draw is 3/4. Hence, the probability of selecting 1 red and 1 white ball is (3/5) * (2/4) + (2/5) * (3/4) = 12/20 = 3/5.
c. Probability of not selecting any red balls:
The probability of not selecting a red ball on the first draw from box A is 2/5. After removing one ball, there are 4 balls left in the box, but none of them are red. So, the probability of not selecting any red balls on the second draw is 4/4 = 1. Hence, the probability of not selecting any red balls is (2/5) * 1 = 2/5.
d. Probability of drawing at least one white ball:
The probability of drawing at least one white ball is the complement of the probability of not selecting any white balls. So, the probability of drawing at least one white ball is 1 - 2/5 = 3/5.