Question

Below, a two-way table is given

for student activities.
Sports Drama Work Total
7
3
13
2
5
5
Sophomore 20
Junior
20
Senior
25
Total
Find the probability the student is in sports,
given that they are a senior.
P(sports | senior) = P(sports and senior)
P(senior)
Round to the nearest whole percent.
=
[? ]%

Answer 1

To find the probability that a student is in sports given that they are a senior, you can use the formula for conditional probability:

P(sports | senior) = P(sports and senior) / P(senior)

From the table, you can see that the number of seniors in sports is 7, and the total number of seniors is 25. So,

P(sports and senior) = 7 / 25

Now, you need to find P(senior), which is the probability that a student is a senior:

P(senior) = Total number of seniors / Total number of students

P(senior) = 25 / 65

Now, you can calculate P(sports | senior):

P(sports | senior) = (7 / 25) / (25 / 65)

To simplify this expression, you can multiply the numerator by the reciprocal of the denominator:

P(sports | senior) = (7 / 25) * (65 / 25)

P(sports | senior) = (7 * 65) / (25 * 25)

P(sports | senior) ≈ 455 / 625

Now, calculate the approximate percentage:

P(sports | senior) ≈ (455 / 625) * 100 ≈ 72.8%

So, the probability that a student is in sports, given that they are a senior, is approximately 72.8%. Rounded to the nearest whole percent, it is 73%.