This table shows how many sophomores and juniors attended two school events. A student is selected randomly from this group. Jazz band concert Volleyball game TotalSophomore 35 42 77Junior 36 24 60Total 71 66 137What is the probability that the student attended the jazz concert, given that the student is a junior?Round your answer to two decimal places.A.0.26B.0.40C.0.51D.0.60SUBMITarrow_backPREVIOUS
Question
This table shows how many sophomores and juniors attended two school events. A student is selected randomly from this group. Jazz band concert Volleyball game TotalSophomore 35 42 77Junior 36 24 60Total 71 66 137What is the probability that the student attended the jazz concert, given that the student is a junior?Round your answer to two decimal places.A.0.26B.0.40C.0.51D.0.60SUBMITarrow_backPREVIOUS
Solution
To find the probability that the student attended the jazz concert given that the student is a junior, we need to use the formula for conditional probability:
P(A|B) = P(A ∩ B) / P(B)
Where:
- P(A|B) is the probability of event A occurring given that event B has occurred.
- P(A ∩ B) is the probability of both events A and B occurring.
- P(B) is the probability of event B occurring.
In this case, event A is the student attending the jazz concert and event B is the student being a junior.
From the table, we can see that:
- The total number of juniors (event B) is 60.
- The number of juniors who attended the jazz concert (event A ∩ B) is 36.
So, we can substitute these values into the formula:
P(A|B) = P(A ∩ B) / P(B) = 36 / 60 = 0.60
Therefore, the probability that the student attended the jazz concert given that the student is a junior is 0.60 or 60%, which corresponds to option D.
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