SOLUTION: the probability that a student passes a physics test is 2/3. of he takes three physics tests, what is the probability that he passes two of the test?

Question 1067876: the probability that a student passes a physics test is 2/3. of he takes three physics tests, what is the probability that he passes two of the test?
Answer by stuylin(8) (Show Source): You can put this solution on YOUR website!
First, we have to know how many cases there are that he passes 2 test, and fails the last test.
Case 1: pass, pass, fail
Case 2: pass, fail, pass
Case 3: fail, pass, pass
So there are 3 cases.
Then we have to take into account of the case when he passes all three:
Case 4: pass, pass, pass
Now, you replace each of these scenarios with the probability.
Case 1: (2/3)*(2/3)*(1/3) = 4/27
Case 2: (2/3)*(1/3)*(2/3) = 4/27
Case 3: (1/3)*(2/3)*(2/3) = 4/27
Case 4: (2/3)*(2/3)*(2/3) = 8/27
Then you add up the probabilities of each of these cases happening:
(4/27)+(4/27)+(4/27)+(8/27) = 20/27
Therefore, the probability that he passes two tests is 20/27.
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