# There Are Three Boys and Two Girls. a Committee of Two is to Be Formed. Find the Probability of the Following Events - Algebra

There are three boys and two girls. A committee of two is to be formed. Find the probability of the following events:
Event A: The committee contains at least one girl
Event B: The committee contains one boy and one girl

#### Solution

Here, there are three boys B1, B2, B3 and two girls G1, G2.
A committee of two is to be formed.
Thus, the sample space (S) is given by
S = {B1B2, B1B3, B2B3, B1G1, B1G2, B2G1, B2G2, B3G1, B3G2, G1G2}
∴n(S) = 10

A is the event that the committee contains at least one girl.
Then, A = {B1G1, B1G2, B2G1, B2G2, B3G1, B3G2, G1G2}
∴n(A) = 7

therefore P(A)=(n(A))/(n(S))

therefore P(A)=7/10

B is the event that the committee contains one boy and one girl.
Then, B = {B1G1, B1G2, B2G1, B2G2, B3G1, B3G2}

therefore P(B)=(n(B))/(n(S))

therefore P(B)=6/10

therefore P(B)=3/5

Concept: Basic Ideas of Probability
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