Question

4) In a poll of 20 high school seniors, 7 took a tech class and 12 took a foods class. 3 students

took both tech and foods. What is the probability that a student took either tech or foods?

Answer 1

The probability that a student took either tech or foods is
`(1)/(5)`

Solution:

In a poll of 20 high school seniors, 7 took a tech class and 12 took a foods class

3 students took both tech and foods

Therefore,

Total number of students = 20

Number of students took tech class alone = 7 - 3 = 4

Number of students took food class alone = 12 - 3 = 9

Number of students both class = 3

Thus,

Number of students took either tech or food = Total number of students - (Number of students took tech class alone + Number of students took food class alone + Number of students both class)

Number of students took either tech or food = 20 - (4+9+3)

Number of students took either tech or food = 20 - 16 = 4

To find: probability that a student took either tech or foods

`probability = \frac{\text{Number of students took either tech or food}}{\text{total number of students}}`

`proability = (4)/(20) = (1)/(5)`

Thus probability that a student took either tech or foods is
`(1)/(5)`