In a high school geometry class, only half of the class earned a passing grade. Out of all the students, 45% studied and passed. What is the probability of the someone having studied, given that they passed?
Question
In a high school geometry class, only half of the class earned a passing grade. Out of all the students, 45% studied and passed. What is the probability of the someone having studied, given that they passed?
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, event A is that a student studied, and event B is that a student passed.
We know that P(A ∩ B), the probability that a student studied and passed, is 45% or 0.45.
We also know that P(B), the probability that a student passed, is 50% or 0.5.
Substituting these values into the formula gives us P(A|B) = 0.45 / 0.5 = 0.9 or 90%.
So, the probability that a student studied given that they passed is 90%.
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