F and G are independent events in sample space S. If Pr(F)=0.45 and Pr(G)=0.6,
find the probability of each of the following events.
What is Pr(F∩G)?
Since F and G are independent, the probability of their intersection is
the product of their probabilities,
Pr(F∩G) = Pr(F)∙Pr(G) = (0.45)(0.6) = 0.27
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What is Pr(F′∩G′)?
Since F and G are independent, so are F' and G', and therefore the
probability of their intersection is likewise the product of their
probabilities, so:
Pr(F') = 1-Pr(F) = 1-0.45 = 0.55
Pr(G') = 1-Pr(G) = 1-0.6 = 0.4
Pr(F'∩G') = Pr(F')∙Pr(G') = (0.55)(0.4) = 0.22
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What is Pr(F′|G′)?
Since the two events F' and G' are independent, the probability
of either one is unchanged when the other event is given, so
Pr(F'|G') = P(F') =0.55
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Edwin
