Q:

Mrs. Daly's reading classes were surveyed about their reading preferences. The data is summarized in the table below. 9th graders who prefer fiction- 359th 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.

Accepted Solution

A:
Answer:Required probability is 0.19Step-by-step explanation:The two-way table for the given data is,                               Fiction                Non-Fiction                Total9th grade                35                            8                             4310th grade               52                            12                           64Total                        87                            20                           107It 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 [tex]P(Non-fiction| 9th\ grade)[/tex].Now, [tex]P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}[/tex]So, we get,[tex]P(Non-fiction| 9th\ grade)=\dfrac{(Non-fiction\bigcap 9th\ grade)}{P(9th\ grade)}\\\\P(Non-fiction| 9th\ grade)=\dfrac{8}{43}\\\\P(Non-fiction| 9th\ grade)=0.19[/tex]Thus, the required probability is 0.19.