# Question Video: Determining the Probability of an Event Mathematics • 7th Grade

A school club has 25 boys and 13 girls. Of the members in the club, 5 of the boys and 4 of the girls wear glasses. If a club member is chosen at random, what is the probability that they do not wear glasses?

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### Video Transcript

A school club has 25 boys and 13 girls. Of the members in the club, five of the boys and four of the girls wear glasses. If a club member is chosen at random, what is the probability that they do not wear glasses?

There are lots of ways of approaching this problem. One way would be to set up a two-way table. The two-way table can be drawn as shown. We are told in the question that there are 25 boys in the club. There are 13 girls in the club. As 25 plus 13 is equal to 38, there are 38 members altogether. We are also told that five of the boys wear glasses. This means that 20 of the boys did not wear glasses as 25 minus five is 20. Four of the girls in the club wear glasses. This means that nine do not. The total number of students that wear glasses is nine as five plus four equals nine. 20 plus nine is equal to 29. Therefore, there are 20 students in the club who do not wear glasses.

We recall that probability can be written as a fraction where the numerator is the number of successful outcomes and the denominator the number of possible outcomes. We need to work out the probability that a student does not wear glasses. There are 29 club members that do not wear glasses. Therefore, our numerator will be 29. The total number of students in the club is 38. Therefore, the denominator is 38. We can therefore conclude that the probability that a club member does not wear glasses is 29 out of 38.