Question

Let C be the event that a randomly chosen adult has some college education. Let M be the event that a randomly chosen adult is married. Given P(C) = .2, P(M) = .6 and P(C ∩ M) = .12, find each probability. (c) Find P(M | C). (Round your answer to 2 decimal places.) P(M | C) (d) Find P(C | M). (Round your answer to 2 decimal places.) P(C | M)

Answer 1

P(M | C) = 0.6.

P(C | M) = 0.2

Explanation:

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

So

P(M | C).

`P(M|C) = (P(M \cap C))/(P(C)) = (0.12)/(0.2) = 0.6`

(d) Find P(C | M).

`P(C|M) = (P(M \cap C))/(P(M)) = (0.12)/(0.6) = 0.2`