Answer:
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%.