Question

In a group of 10 boys and 11 girls, 2 members are selected. What is the probability to select 2 boys?10.50.15260.2142

Answer 1

Given:

The 2 boy selected out of 10 then boy selecting is:

`=^(10)C_2`

Then favorable outcome is:

`\begin{gathered} =^(10)C_2 \\ =(10!)/((10-2)!2!) \\ =(10*9*8!)/(8!*2*1) \\ =(90)/(2) \\ =45 \end{gathered}`

Total outcome is:

`\begin{gathered} =^(21)C_2 \\ =(21!)/((21-2)!2!) \\ =(21*20*19!)/(19!*2*1) \\ =(21*20)/(2) \\ =210 \end{gathered}`

Probability is define as:

`\begin{gathered} P(a)=\frac{\text{ favorable outcome}}{\text{ total outcome}} \\ P(a)=(45)/(210) \\ =0.2142 \end{gathered}`