Probabilities are used to determine the chances of an event.
The probability that both selections are boys is 0.1667
The given parameters are:
[tex]\mathbf{Boys = 35}[/tex]
[tex]\mathbf{Girls = 50}[/tex]
[tex]\mathbf{Total= 85}[/tex]
Since two are chosen to sing a duet, then the selection is without replacement.
So, the probability that both selections are boys is:
[tex]\mathbf{Pr = \frac{Boys}{Total} \times \frac{Boys-1}{Total-1}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{35}{85} \times \frac{35-1}{85-1}}[/tex]
Subtract
[tex]\mathbf{Pr = \frac{35}{85} \times \frac{34}{84}}[/tex]
Divide
[tex]\mathbf{Pr = 0.4118 \times 0.4048}[/tex]
[tex]\mathbf{Pr = 0.1667}[/tex]
Hence, the probability that both selections are boys is 0.1667
Read more about probabilities at:
https://brainly.com/question/11234923
