Question

Given the following *joint probability distribution*, P(A,B), for A and B,

	a1	a2
b1	0.37	0.16
b2	0.23	0.24

Calculate the marginal probability distribution, P(B).

Calculate the conditional probability distribution, P(A|B).

Answer 1

Let's find the marginal distribution of A

P(A = a1) = 0.37 + 0.23 = 0.60

P(A = a2 ) = 0.16 + 0.24 = 0.40

So the marginal distribution of A is as follows:

A	a1	a2	Total
P(A)	0.60	0.40	1

Let's find conditional distribution of A|B

for B = b1

P(A = a1 | B = b1) = 0.37/(0.37+0.16) = 0.6981

P(A = a2 | B = b1) = 0.16/(0.37+0.16) = 0.3019

A|B=b1	a1	a2	Total
P(A|B=b1)	0.6981	0.3019	1

for B = b2

P(A = a1 | B = b2) = 0.23/(0.23+0.24) = 0.4894

P(A = a1 | B = b2) = 0.24/(0.23+0.24) = 0.5106

A|B=b2	a1	a2	Total
P(A|B=b2)	0.4894	0.5106	1