Two boys and 3 girls were selected for the finals of a dance contést. One of the three different prizes marked A. B and C will be randomly awarded to the 5 contestants whose name is selected to win. Find the probability that the boy will win the prize marked B?

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)

2? if not the correct answer you might need to provide more information

step-by-step explanation: