Answer:
(a) P(A ∩ E) = 0.03
(b) P(A) = 0.39
(c) P(A | E) = 0.1
Explanation:
The first level of the tree gives the following probabilities
P(E) = 0.1
P(E') = 1 - P(E) = 0.9
The second level gives conditional probabilities
P(A|E) = 0.3 this is the top most branch from the root
P(A ∩ E) = P(A|E) P(E) = 0.3 x 0.1 = 0.03 Answer(a)
To find P(A) we find all routes that will end in A, compute each probability and add up the individual probabilities
For event E happening, P(A ∩ E) = 0.03 which is computed in A
However A can also happen when the complement event E' happens
P(A ∩ E') = P(A | E') P(E') = 0.4 x 0.9 = 0.36
Add these two together to get 0.03 + 0.36 = 0.39 Answer (b)
P(A|E) is nothing but the probability value when we follow the E branch first followed by the A branch
This is 0.1 answer (c)