
34 Data Analysis and Statistics for Geography, Environmental Science, and Engineering
If events A and C are independent, then P[C|A] is just P[C] and therefore
PACPCAPC PCPA[] = [ |][] = [ ][]
(2.9)
Example: Consider a sequence of two tosses of a fair coin. In the first toss define event
A= {heads in first toss}, with P[A] = 0.5 and event C = {heads in second toss}. What is
the probability of getting a head in both tosses? The probability of getting a head inthe
second toss is independent of whatever we got in the rst toss, thus P[C|A] = P[C]=0.5.
In this case, the event AC = {head the first toss AND head the second toss}. Then,
calculate ...