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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?

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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%.

This problem has been solved

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