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$A class is made up of 4 boys and 10 girls. Half of the girls wear glasses. A student is selected at random from the class. What is the probability that the student is a girl with glasses? Write your answer as a fraction in simplest form.$

A class is made up of $4$ boys and $10$ girls. Half of the girls wear glasses. A student is selected at random from the class. What is the probability that the student is a girl with glasses? $\newline$ Write your answer as a fraction in simplest form.

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Theoretical probability

Full solution

Q. A class is made up of

4

boys and

10

girls. Half of the girls wear glasses. A student is selected at random from the class. What is the probability that the student is a girl with glasses?

\newline

Write your answer as a fraction in simplest form.

Calculate total number of students: Calculate the total number of students in the class. There are $4$ boys and $10$ girls, so the total number of students is $4 + 10 = 14$ .
Determine girls with glasses: Determine the number of girls who wear glasses. Half of the $10$ girls wear glasses, so $10 / 2 = 5$ girls wear glasses.
Calculate probability for girl with glasses: Calculate the probability that a randomly selected student is a girl with glasses. The probability is the number of girls with glasses divided by the total number of students, so $P(\text{girl with glasses}) = \frac{5}{14}$ .

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