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Chapter 2
nl which is P(E1, E2) probability of El followed by E2. We have
P(EI + E2) = P(E~) P(E2) - P(E1, E2) again Eq. (2 .2).
Before proceeding to Bayes theorem it is known
P(A) + P(~l)
Lets take the rocket shots Example 2.1
P(A_) = 0.20 probability of success
P(A) = 1 - 0.20 = 0.80 probability of failure.
(2.4)
II. BAYES THEOREM
Lets now consider two events which are not independent or
P(AB) = P(A)P(B/A)
also
P(BA) -- P(B)P(A/B)
using Eqs. (2.5) and (2.6)
P(A)P(B/A)
P(A/B)
P(a)
Some definitions are in order.
P(AB)
P(A)
P(B)
P(B/A)
P(A / B)
(2.5)
(2.6)
(2.7)
The probability that "A" happened followed by B.
It is not known whether or not "B" happened. P(A) is the
probability that "A" did.
It is not known whether or not "A" happened. P(B) is the
probability that "B" did.
"A" is known to have happened. This is the probability that it
was followed by "B".
"B" is known to have happened. This is the probability that it
was followed by "A".
Now noting Eq. (2.4)
P(A) + P(~)
B must occur with A or ~ so
P(B) = P(AB) + P(~IB)