Question

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

Answer 1

`\frac{\textbf{1}}{\textbf{20}}`

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=
`(7)/(8+11+9+7)=(7)/(35)=(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=
`(9)/(10+7+10+9)=(9)/(36)=(1)/(4)`

For two independent events,

Probability for both event 1 and event 2 to take place=
`\text{probability of event 1} * \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}*\text{probability for girl to be senior}`

Probability for both boy and girl chosen to be senior=
`(1)/(5) * (1)/(4) = (1)/(20)`

So,required probability is
`(1)/(20)`