Question

Mrs. Daly's reading classes were surveyed about their reading preferences. The data is summarized in the table below.

9th graders who prefer fiction- 35
9th graders who prefer nonfiction- 8
total of 9th graders- 43
10th graders who prefer fiction- 52
10th grader who prefer nonfiction- 12
total of 10th graders-64
total of students who prefer fiction-87
total of student who prefer nonfiction-20
total of students- 107
Given that a student is in 9th grade, what is the probability that they prefer to read non-fiction novels based on this data? Write your answer as a decimal rounded to the nearest hundredth.

Answer 1

0.19

Explanation:

Answer 2

Required probability is 0.19

Explanation:

The two-way table for the given data is,

Fiction Non-Fiction Total

9th grade 35 8 43

10th grade 52 12 64

Total 87 20 107

It is required to find the probability of the students who prefer to read non-fiction novels, given that they are in 9th grade.

That is, to find the conditional probability
`P(Non-fiction| 9th\ grade)`.

Now,
`P(A|B)=(P(A\bigcap B))/(P(B))`

So, we get,

`P(Non-fiction| 9th\ grade)=((Non-fiction\bigcap 9th\ grade))/(P(9th\ grade))\\\\P(Non-fiction| 9th\ grade)=(8)/(43)\\\\P(Non-fiction| 9th\ grade)=0.19`

Thus, the required probability is 0.19.