Let S be the event that a randomly selected college student has taken a statistics course, and let C be the event that the same student has taken a chemistry course. Suppose P(S)=0.4, P(C)=0.3, and P(S ? C)=0.2.
a. Find the probability that a student has taken statistics, chemistry, or both.
b. Find the probability that a student has taken neither statistics nor chemistry.
c. Find the probability that a student has taken statistics but not chemistry.
(a) P(S
C) =P(S) + P(C) ? P(S ? C)
= 0.4 + 0.3 ? 0.2
= 0.5
(b) 
= 1?P(S 
C) = 1?0.5 = 0.5.
(c) We need to find 
. Now P(S) = P(S ? C) + 
(this can be seen from a Venn diagram). Now
P(S ? C)=P(S) + P(C) ? P(S 
C)
=0.4 + 0.3 ? 0.5
=0.2
Since P(S) = 0.4 and P(S ? C) = 0.2, 
= 0.2.
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