Question

12.what is the probability that a boy and a girl chosen randsomly will be seniors?

Answer 1

$\frac{\textbf{1}}{\textbf{20}}$

Step-by-step explanation:

Probability=$\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$

Probability for a randomly chosen girl to be senior=$\frac{\text{number of senior girls}}{\text{total number of girls}}$

Probability for a randomly chosen girl to be senior=$\frac{7}{8+11+9+7}=\frac{7}{35}=\frac{1}{5}$

Probability for a randomly chosen boy to be senior=$\frac{\text{number of senior boys}}{\text{total number of boys}}$

Probability for a randomly chosen girl to be senior=$\frac{9}{10+7+10+9}=\frac{9}{36}=\frac{1}{4}$

For two independent events,

Probability for both event 1 and event 2 to take place=$\text{probability of event 1} \times \text{probability of event 2}$

Since choosing boys and girls is independent,

Probability for both boy an girl chosen to be senior=$\text{probability for boy to be senior}\times\text{probability for girl to be senior}$

Probability for both boy and girl chosen to be senior=$\frac{1}{5} \times \frac{1}{4} = \frac{1}{20}$

So,required probability is $\frac{1}{20}$