A test was given to a group of students. The grades are shown below. Find the probability that a student chosen at random was a female.
| | A | B | C | Total |
| :---- | :- | :- | :- | :---- |
| Male | 8 | 18 | 13 | 39 |
| Female| 10 | 4 | 12 | 26 |
| Total | 18 | 22 | 25 | 65 |
A. $3 / 7$
B. $2 / 5$
C. $2 / 3$
D. $3 / 4$
Answer (1)
Find the total number of students: 65.
Find the number of female students: 26.
Divide the number of female students by the total number of students: 65 26 .
Simplify the fraction: 65 26 = 5 2 .
Explanation
Understand the problem We are given a table that shows the grades of male and female students. We want to find the probability that a student chosen at random is a female.
Identify the total number of students and female students From the table, we can see that the total number of students is 65. The number of female students is 26.
Calculate the probability To find the probability that a student chosen at random is a female, we divide the number of female students by the total number of students: 65 26 We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 13: 65 ÷ 13 26 ÷ 13 = 5 2
State the final answer Therefore, the probability that a student chosen at random was a female is 5 2 .
Examples
In a school, you might want to know the probability of randomly selecting a female student to represent the student body. This helps ensure fair representation in activities or surveys. For example, if a school has 65 students and 26 are female, the probability of picking a female student at random is 65 26 , which simplifies to 5 2 or 40%.
