Let PA PB 13 and PA B 110 Find the following PA B PA B P

Let P(A) = P(B) = 1/3 and P(A B) = 1/10. Find the following: P(A B) P(A | B) P(\'A B\') Are A and B disjoint events? Are they independent? Justify your answers.

Solution

a)

P(A U B) = P(A) + P(B) - P(A n B) = 1/3 + 1/3 - 1/10 = 17/30 [answer]

b)

P(A|B) = P(A n B) / P(B) = (1/10) / (1/3) = 3/10 [answer]

c)

P(A\' U B\') = 1 - P(A n B) = 1 - 1/10 = 9/10 [answer]

d)

A and B are not disjoin as P(A n B) =/= 0.

They are not independent as P(A n B) =/= P(A) P(B).