A class contains 59 students. In the class, the number of boys exceeds the number of girls by seven. If a student is chosen at random, what is the probability the student is a boy?
In this question, we are told that a class contains 59 students. We want to calculate the probability that a randomly selected student, where each
student is equally likely to be chosen, is a boy. Let’s begin by calculating the number of boys in the class. We will let 𝑥 be the number of boys in the class. We are told that the number of boys exceeds the number of girls by seven. This means that there are seven more boys than girls, and as such, the number of
girls is equal to 𝑥 minus seven. Recall that the total number of students is 59. So, 𝑥 plus 𝑥 minus seven equals 59.
The left-hand side of our equation simplifies to two 𝑥 minus seven. We can then solve for 𝑥 by firstly adding seven to both sides. This gives us two 𝑥 is equal to 66. Dividing through by two, we have 𝑥 is equal to 33. This means that there are 33 boys and 26 girls, which gives us a total of 59
students. Next, we recall that the probability of an event can be written as the number of
favorable outcomes over the total number of possible outcomes. Note that this holds when every item is equally likely to be selected as in this
case. As such, the probability that a chosen student from the class selected at random is a
boy is 33 out of 59.