# Question Video: Determining Conditional Probabilities

A math teacher gave her class two tests. 55% of the class passed both tests, and 65% of the class passed the first test. What percent of those who passed the first test also passed the second test? Round your answer to the nearest integer if necessary.

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### Video Transcript

A math teacher gave her class two tests. 55 percent of the class passed both tests, and 65 percent of the class passed the first test. What percent of those who passed the first test also passed the second test? Round your answer to the nearest integer, if necessary.

So, we have these two events: passing the first test, pass one, and passing the second test, pass two. We’re told that the probability of passing the first test is 65 percent and the probability of passing both tests is 55 percent. We’re asked to find what percent of those who passed the first test also passed the second test. If we rephrase this question as what percent passed the second test given they had passed the first test, then we can see more clearly that we have a conditional probability.

When we need to find the probability of an event 𝐴 given an event 𝐵, we find the probability of 𝐴 intersection 𝐵 divided by the probability of 𝐵. So, to find the probability of passing the second test given the first test was passed, we find the probability of passing both tests divided by the probability of passing the first test. We can then simply plug in values that we have.

The probability of passing both tests is 55 percent, and the probability of passing the first test is 65 percent. As we can give our answer to the nearest integer, we can assume that a calculator can be used. And this would give us the decimal value of 0.84615 and so on. In order to give the value as a percentage, we multiply by 100 which gives us 84.615 and so on percent.

We then need to make sure the answer is rounded to the nearest integer. So, we check the first decimal digit to see if it’s five or more. And as it is, then it rounds up to 85 percent. So, the answer is that 85 percent of the students who passed the first test also passed the second test.