A survey was given to 90
high school students. They were asked if they preferred fiction or non-fiction and if they preferred indoor or outdoor activities. Partial survey results are shown in the table.
Fiction Non-Fiction Total
Indoor 24
50
Outdoor 30
Total 90
What percent of students in the survey, to the nearest whole number, prefer outdoor activities given they prefer non-fiction?
Enter a number in the box.
P(outdoor | non−fiction)=
%
To find the percentage of students who prefer outdoor activities given they prefer non-fiction, we need to divide the number of students who prefer outdoor activities and non-fiction by the total number of students who prefer non-fiction.
From the table, we can see that the number of students who prefer outdoor activities and non-fiction is 30.
The total number of students who prefer non-fiction is 50.
To find the percentage, we divide 30 by 50 and multiply by 100:
P(outdoor | non-fiction) = (30/50) * 100 = 60%
Therefore, approximately 60% of students in the survey prefer outdoor activities given they prefer non-fiction.
To find the percentage of students who prefer outdoor activities given they prefer non-fiction, we need to use the conditional probability formula:
P(A|B) = P(A and B) / P(B)
Here, A represents "preferring outdoor activities" and B represents "preferring non-fiction".
From the table, we can see that there are 50 students who prefer non-fiction. Therefore, P(B) = 50/90.
We also see that 30 students prefer outdoor activities and non-fiction. Therefore, P(A and B) = 30/90.
Now we can substitute these values into the formula:
P(A|B) = (30/90) / (50/90)
Simplifying, P(A|B) = 30/50
To find the percentage, we can multiply this fraction by 100 and round it to the nearest whole number:
P(outdoor | non-fiction) ≈ (30/50) * 100 ≈ 60%
Therefore, approximately 60% of the students in the survey prefer outdoor activities given they prefer non-fiction.