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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