A science class has 5 girls and 5 boys in the seventh grade and 3 girls and 1 boy 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?Write your answer as a fraction in simplest form.
Question
A science class has 5 girls and 5 boys in the seventh grade and 3 girls and 1 boy 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?Write your answer as a fraction in simplest form.
Solution
To solve this problem, we need to calculate the probability of each event separately and then multiply them together.
First, let's calculate the probability of selecting a boy from the seventh grade. There are 5 boys and 5 girls in the seventh grade, making a total of 10 students. So, the probability of selecting a boy is 5 out of 10, or 1/2.
Next, let's calculate the probability of selecting a boy from the eighth grade. There are 1 boy and 3 girls in the eighth grade, making a total of 4 students. So, the probability of selecting a boy is 1 out of 4, or 1/4.
Finally, to find the probability of both events happening (selecting a boy from the seventh grade and selecting a boy from the eighth grade), we multiply the probabilities together.
So, the probability is (1/2) * (1/4) = 1/8.
Therefore, the probability that the teacher selects two boys is 1/8.
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