Question

The probability of passing the math class of Professor Goodrum is 59%, the probability of passing Professor Cruise's physics

class is 26%, and the probability of passing both is 17%. What is the probability of passing one or the other?
(Give your answer as a whole percent number.)
probability of passing one or the other:

Answer 1

51%

Explanation:

Given P(passing math) = 59%, P(passing physics) = 26%, and P(passing both) = 17%, you want to find the probability of passing only one of the courses.

Probability relations

We can record the given probabilities in a 2-way table (values shown in blue). The table is completed by making sure the totals add up (values shown in black).

The probability of passing one course and failing the other is the sum of the probabilities with a yellow background:

42% +9% = 51%

The probability of passing one or the other is 51%.

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Additional comment

We can also get there using the relation ...

P(A+B) = P(A) +P(B) -P(AB)

The union of A and B also includes their overlap:

P(A+B) = P(AB') +P(A'B) +P(AB)

In other words, the probability of interest is ...

P(AB') +P(A'B) = P(A) +P(B) -2×P(AB) = 59% +26% -2(17%)

P(AB') +P(A'B) = 51%