Question

Of 20 computers in a cluster room, 12 have the mathematical package Mathematica, 5 have the mathematical package Maple, and 6 have neither package. A student enters the cluster room and chooses a computer at random. Find the probability of each of the following events:

(a) the chosen computer has at most one of the two packages >>> my answer for this is %55 but the true answer is %15 why ??
(b) the chosen computer has exactly one of the two packages. >>> my answer for this is %55 my answer for this was correct

so my question is why (a) and (b) have different answers though they asking same question but in different way

Answer 1

Total = A + B - Both + neither

Therefore Computers who have both packages = 12 + 5 + 6 - 20 = 3

Therefore the Number of computers who have only Mathematica = A - Both = 12 - 3 = 9

The Number of computers who have only Maple = B - Both = 5 - 3 = 2

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(a) P(At Most 1) = (Number of computers which have exactly 1 package + those who have neither package) / Total computers = (9 + 2 + 6) / 20 = 17 / 20 = 85%

(b) P(Exactly 1) = (9 + 2) / 20 = 55%

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