Mutually exclusive events

Question

Let A and B be two mutually exclusive events. The P(A)=.4 and the P(B)=.2  Compute all of the following

 

a) P(A intersection B)

b) P(A^c)

c) P(A U B)

d) P(B^c)

e) P(A^c intersection B^c)

Answer 1

By definition, mutually exclusive events do NOT have an intersection. 

a) P(A intersection B) = 0

b) P(Ac) = 1 -.4 = .6

This is true regardless of whether or not the events are mutually exclusive. 

 

c) P(A U B) = .4 + .2 = .6

For mutually exclusive event, you may just add the probabilities of A and B together to find the union - since there is no intersection. 

 

d) P(Bc) = 1 - .2 = .8

This is true regardless of whether or not the events are mutually exclusive.

e) P(Ac intersection B) = P(B) = .2