a math teach gave her students two tests. on the first test, 64% of the class passed the test, but only 40% of the class lassed both tests. What is the probablity that a student passes the second test given they passed the first one?
Ms. sue or Steve help!
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To find the probability that a student passes the second test given they passed the first one, we need to use conditional probability.
Let's denote the event "passing the first test" as A and the event "passing the second test" as B.
We are given that 64% of the class passed the first test, so P(A) = 0.64.
We are also given that only 40% of the class passed both tests, so P(A ∩ B) = 0.40.
We can use the formula for conditional probability as follows:
P(B|A) = P(A ∩ B) / P(A)
Substituting the given values, we get:
P(B|A) = 0.40 / 0.64
P(B|A) ≈ 0.625
Therefore, the probability that a student passes the second test given they passed the first one is approximately 0.625 or 62.5%.
To find the probability that a student passes the second test given they passed the first one, you can use conditional probability. Conditional probability calculates the probability of an event (passing the second test) given that another event has already occurred (passing the first test).
Let's break down the information given:
- 64% of the class passed the first test.
- 40% of the class passed both tests.
To find the probability that a student passes the second test given they passed the first one, we need to calculate the percentage of students who passed both tests out of the students who passed the first test.
First, we need to calculate the percentage of students who passed the first test but not the second test. Since 40% of the class passed both tests, the remaining percentage of students who passed the first test but not the second test would be 64% - 40% = 24%.
Therefore, the probability that a student passes the second test given they passed the first one would be the percentage of students who passed both tests (40%) divided by the percentage of students who passed the first test (64%).
To calculate this probability, we divide 40% by 64%:
P(passing the second test | passing the first test) = 40% / 64%
So the probability that a student passes the second test given they passed the first one is 40% / 64%.
recall that P(A|B) = P(A&B)/P(B)
now plug in your numbers