The probability that the second ball drawn is black is 4/10 = 2/5
There are two cases. The case where the first ball is red is the first one.
The probability of drawing a red ball is equal to the quotient between the number of red balls and the total number of balls.
p = 3/5
Then, the probability of drawing a black ball in the second attempt is computed in the same way, but because we already drew a ball, now the total number of balls is 4, so we have:
q = 2/4 = 1/2.
So the joint probability is:
P = (3/5)*(1/2) = 3/10.
Then we have the case where both balls are black, the probabilities now are:
p = 2/5
q = 1/4
So the joint probability is:
P = (2/5)*(1/4) = 1/10
The total probability is the sum of the two above:
probability = 3/10 + 1/10 = 4/10.
The probability that the second ball drawn is black is 4/10 = 2/5
If you want to learn more about probability:
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