Answer:
2 boys and 3 girls were selected for the finals.
There are 3 prizes, A, B, and C (assigned in order, I suppose) assigned randomly to the five contestants.
We want to find the probability that a boy wins the prize B.
So here we have two cases:
A girl wins the first prize, A, and a boy the prize B.
The probability that a girl wins the prize A is equal to the quotient between the number of girls and the total number of contestants, this is:
p = 3/5
Next, the probability that a boy wins the prize B, is equal to the quotient between the number of boys and the total number of contestants (that now is 4, because a girl already won prize A).
q = 2/4
The joint probability is:
P = p*q = (3/5)*(2/4) = 6/20 = 3/10
Now we have the other case, where a boy wins the prize A and the other boy wins prize B.
The probability that a boy wins prize A is equal to the quotient between the number of boys and the total number of contestants, this is:
p = 2/5
The probability that the other boy wins prize B is equal to the quotient between the remaining number of boys (1) and the total number of contestants (now 4), this is:
q = 1/4
The joint probability is:
P' = p*q = (2/5)*(1/4) = 2/20 = 1/10
The total probability is the sum of the probabilities for the two cases, this is:
Probability = 1/10 + 3/10 = 4/10
(note that because the prize C is assigned after prize B, its existence does not affect the probability for the previous event, as expected)