The probability of male given senior can be given the formula:
[tex]P(male\text{ \mid senior\rparen = }\frac{P(male\text{ and senior\rparen}}{P(senior)}[/tex]
Recall the probability of an event e can be calculated using the formula:
[tex]P(an\text{ event e occurring\rparen= }\frac{Number\text{ of expected outcomes}}{Total\text{ number of possible outcomes}}[/tex]
From the table, we have:
Total number of students = 30
Total number of seniors = 5
Total number of males that are seniors = 2
Substituting the values into the formula:
[tex]\begin{gathered} P(male\text{ \mid Senior\rparen = }\frac{\frac{2}{30}}{\frac{5}{30}} \\ =\text{ 0.4} \\ Converting\text{ to \%} \\ P(male\text{ \mid Senior\rparen = 40\%} \end{gathered}[/tex]
Answer: 40%
