Answer:
The probability of picking at least three boys is [tex]\frac{5}{41}[/tex] .
Step-by-step explanation:
We have to choose 5 people to form a student government.
We have to pick 5 people out of 7 girls and 5 boys.
What is the probability that at least 3 boys are a part of the student government?
The probability of picking 5 people out of 12 girls and boys = [tex]\frac{5}{12}[/tex]
The probability of picking at least 3 boys excludes the probability of picking 3 girls. The probability of picking 3 girls = [tex]\frac{3}{7}[/tex]
The probability of picking at least 3 boys = 1 - [tex]\frac{3}{7}[/tex] = [tex]\frac{2}{7}[/tex]
The probability of picking 5 people and the probability of picking at least 3 boys = [tex]\frac{5}{12}[/tex] × [tex]\frac{2}{7}[/tex] = [tex]\frac{5}{41}[/tex]
