Question

An exam has two probability problems, 1 and 2. If 37% of the students solved problem 1 and 12% of the students solved both problems 1 and 2, what percent of the students who solved problem 1 also solved problem 2?

Answer 1

about 32%

Explanation:

The desired probability is the conditional probability that problem 2 was solved given that problem 1 was solved. That is ...

P(2|1) = P(1&2)/P(1) = 12%/37% ≈ .324 ≈ 32%

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You can also think of it like this. If there were 100 students taking the exam, 37 solved the first problem. Of those 37, 12 solved the second one. 12 is about 32% of 37.