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A computer science teacher is trying to build a midterm test. There are three pools of...

A computer science teacher is trying to build a midterm test. There are three pools of problems, each pool has problems from two categories: extremely difficult or extremely easy, no other options. 12 problems have been borrowed from pool 1, 20 problems were borrowed from pool 2 and 18 problems were borrowed from pool 3. 90% of all problems in pool 1 are extremely difficult. There are 60% of such difficult problems in pool 2 and 90% in pool 3. Find the total probability that a problem is extremely difficult.

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