At Monroe High School, 62% of all students participate in after-school sports and 11% participate in both after-school sports and student council. What is the probability that a student participates in student council given that the student participates in after-school sports?A.7%B.18%C.15%D.11%
Question
At Monroe High School, 62% of all students participate in after-school sports and 11% participate in both after-school sports and student council. What is the probability that a student participates in student council given that the student participates in after-school sports?A.7%B.18%C.15%D.11%
Solution
To solve this problem, we need to use the formula for conditional probability, which is P(A|B) = P(A ∩ B) / P(B).
In this case, we want to find the probability that a student participates in student council given that the student participates in after-school sports.
So, event A is that a student participates in student council and event B is that a student participates in after-school sports.
From the problem, we know that P(A ∩ B) = 11% or 0.11 (the probability that a student participates in both after-school sports and student council) and P(B) = 62% or 0.62 (the probability that a student participates in after-school sports).
Substituting these values into the formula gives us:
P(A|B) = P(A ∩ B) / P(B) = 0.11 / 0.62 = 0.1774 or 17.74%
So, the probability that a student participates in student council given that the student participates in after-school sports is approximately 18%. Therefore, the correct answer is B. 18%.
Similar Questions
At Taft High School, 59% of all students participate in after-school sports and 23% participate in both after-school sports and volunteer activities. What is the probability that a student participates in volunteer activities given that the student participates in after-school sports?A.36%B.82%C.59%D.39%
At Howard High School, 53% of all students participate in after-school sports and 27% participate in both after-school sports and music lessons. What is the probability that a student participates in music lessons given that the student participates in after-school sports?A.80%B.26%C.51%D.14%SUBMITarrow_backPREVIOUS
At Jefferson Middle School, 12% of the students play volleyball and 5% of the students play volleyball and basketball. What is the probability that a student plays basketball given that he or she plays volleyball?A.0.6%B.24%C.41.7%D.6%SUBMITarrow_backPREVIOUS
At Franklin High School, 15% of the students play basketball and 4% of the students play baseball and basketball. What is the probability that a student plays baseball given that he or she plays basketball?A.37.5%B.26.7%C.6%D.0.6%
At a high school, 18% of the students play football and 6% of the students play football and baseball. What is the probability that a student plays baseball given that he plays football?A.1.1%B.3%C.33.3%D.10.8%SUBMITarrow_backPREVIOUS
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.