Question

A science class has girls and boys in the seventh grade and girls and boys in the eighth grade. The teacher randomly selects a seventh grader and an eighth grader from the class for a competition. What is the probability that the students she selects are both boys?

Answer 1

Probability of randomly selecting both students as boys is $(\frac{5}{24})$

Step-by-step explanation:

Here, the given question is  incomplete .

A math class has 4 girls and 4 boys in the seventh grade and 7 girls and 5 boys in the eighth grade. The teacher randomly selects a seventh grader and an eighth grader from the class for a competition. What is the probability that the students she selects are both boys?

Solving the given question we get:

The total number of girls in the 7th grade  = 4

The total number of boys in the 7th grade  = 4

So, the probability of selecting a boy in 7th grade  = $\frac{\textrm{Total number of boys}}{total students in 7th grade} = \frac{4}{4+4} = \frac{1}{2}$    .... (1)

The total number of girls in the 8th grade  = 7

The total number of boys in the 8th grade  = 5

So, the probability of selecting a boy in 8th grade  = $\frac{\textrm{Total number of boys}}{total students in 8th grade} = \frac{5}{5+7} = \frac{5}{12}$    .... (2)

Now, combination of both the probabilities, we get:

The  probability that both  students selected are boys  = $\frac{1}{2} \times \frac{5}{12} = \frac{5}{24}$

Hence, probability of randomly selecting both students as boys is $(\frac{5}{24})$