[tex]\frac{\textbf{1}}{\textbf{20}}[/tex]
Step-by-step explanation:
Probability=[tex]\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}[/tex]
Probability for a randomly chosen girl to be senior=[tex]\frac{\text{number of senior girls}}{\text{total number of girls}}[/tex]
Probability for a randomly chosen girl to be senior=[tex]\frac{7}{8+11+9+7}=\frac{7}{35}=\frac{1}{5}[/tex]
Probability for a randomly chosen boy to be senior=[tex]\frac{\text{number of senior boys}}{\text{total number of boys}}[/tex]
Probability for a randomly chosen girl to be senior=[tex]\frac{9}{10+7+10+9}=\frac{9}{36}=\frac{1}{4}[/tex]
For two independent events,
Probability for both event 1 and event 2 to take place=[tex]\text{probability of event 1} \times \text{probability of event 2}[/tex]
Since choosing boys and girls is independent,
Probability for both boy an girl chosen to be senior=[tex]\text{probability for boy to be senior}\times\text{probability for girl to be senior}[/tex]
Probability for both boy and girl chosen to be senior=[tex]\frac{1}{5} \times \frac{1}{4} = \frac{1}{20}[/tex]
So,required probability is [tex]\frac{1}{20}[/tex]
