Events A1, A2 and A3 form a partiton of the sample space S with probabilities P(A1) = 0.3, P(A2) = 0.5, P(A3) = 0.2.
If E is an event in S with P(E|A1) = 0.1, P(E|A2) = 0.6, P(E|A3) = 0.8, compute

a. P(E) =
b. P(A1|E) =
c. P(A2|E) =
d. P(A3|E) =

a. By the law of total probability,

and using the definition of conditional probability we can expand the probabilities of intersection as

b. Using Bayes' theorem (or just the definition of conditional probability), we have

c. Same reasoning as in (b):

d. Same as before:

(Notice how the probabilities conditioned on add up to 1)

image result for what is another name for consecutive interior angles? ​

when two lines are crossed by another line (called the transversal): the pairs of angles on one side of the transversal but inside the two lines are called consecutive interior angles. in this example, these are consecutive interior angles: d and f.

step-by-step explanation:

just sum

10 + 10 = 20