Question

there are 15 boys and some girls in a class. the total number of students is 24. a student is randomly selected to be a proctor.

1. what is the probability that the selected student is a boy?
2. what is the probability that the selected student is not a boy?

Explanation:

Step1: Calculate the number of girls

The total number of students is \(24\), and the number of boys is \(15\). So the number of girls is \(24 - 15=9\).

Step2: Calculate the probability of selecting a boy

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
For selecting a boy, the number of favorable outcomes (number of boys) is \(15\), and the total number of outcomes (total number of students) is \(24\). So the probability \(P(\text{boy})=\frac{15}{24}=\frac{5}{8}\).

Step3: Calculate the probability of not selecting a boy

The probability of not selecting a boy is equal to the probability of selecting a girl.
The number of favorable outcomes (number of girls) is \(9\), and the total number of outcomes (total number of students) is \(24\). So the probability \(P(\text{not boy})=\frac{9}{24}=\frac{3}{8}\).

Answer:

1. \(\frac{5}{8}\)
2. \(\frac{3}{8}\)