Question

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

Answer 1

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`