The probability that Adam succeeding mathematics is 0.33, the probability of him failing Physics is 0.32, and the probability of him succeeding in one of them at least is 0.71. Find the probability that Adam succeeding ONLY one of the two subjects.
In this case, event is Adam succeeding in mathematics, and
event is Adam succeeding in physics. This means that event
is Adam failing in physics. The events and
are complementary, so the sum of their probabilities
is equal to 1. First, use this fact to find the probability of
The notation refers to the probability of either
event or event occurring, or both. In other words, the
notation refers to the probability of at least one of
the events occurring. If and are two non-mutually
exclusive events, then , where
the notation refers to the probability of events
and occurring together. Now use this fact to find .
The probability of only one of the two events and
occurring is the difference of and .
Next, find the difference of and .
Thus, the probability of Adam succeeding in only one of the two
subjects is 0.41.