A math class has
7
girls and
5
boys in the seventh grade and
4
girls and
4
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?
Write your answer as a fraction in simplest form.
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To find the probability that the students she selects are both boys, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes: This can be found by multiplying the number of choices for the first student (which is 12 – 7 = 5, as there are 7 girls and 5 boys in the seventh grade) by the number of choices for the second student (which is 8 – 4 = 4, as there are 4 girls and 4 boys in the eighth grade). So, the total number of possible outcomes is 5 * 4 = 20.
Number of favorable outcomes: In this case, the teacher needs to select two boys. The number of choices for the first student (boy) is 5, and the number of choices for the second student (also a boy) is 4. So, the number of favorable outcomes is 5 * 4 = 20.
Therefore, the probability that the students she selects are both boys is 20/20, which simplifies to 1/1 or simply 1.
To find the probability that the teacher selects two boys, we need to calculate the total number of possible outcomes and the number of favorable outcomes.
First, let's find the total number of possible outcomes. The teacher can randomly select one student from the seventh grade, and then from the eighth grade. Since there are 7 girls + 5 boys = 12 students in the seventh grade, and 4 girls + 4 boys = 8 students in the eighth grade, there are a total of 12 * 8 = 96 possible outcomes.
Now, let's find the number of favorable outcomes, which is the number of ways the teacher can select two boys. There are 5 boys in the seventh grade and 4 boys in the eighth grade, so the number of favorable outcomes is 5 * 4 = 20.
Therefore, the probability of selecting two boys is 20/96.
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4. Dividing 20 by 4 gives us 5, and dividing 96 by 4 gives us 24.
So, the probability of selecting two boys is 5/24.
grade7: 7girls, 5 boys
grade8: 4 girls, 4boys
prob(boy from gr7 and boy from gr8)
= (5/12)(4/8) = 5/24