Mutually exclusive events

Question

Let A and  be two mutually exclusive events. The P(A)= .37 and the P(B)= .24   Compute all of the following:

 

a) P(A intersection B)

b) P(B^c)

c) P(A U B)

d) P(A^c)

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

Answer 1

a) Since they are mutually exclusive, they cannot both happen.  Therefore P (A∩B) = 0

 

b) I assume that the c superscript means "complement" which means the probability of the event NOT happening?  If so, then P(B^c) = 1 - P(B) = .76

 

c) P(A U B) = P(A) + P(B) - P(A∩B) = .37 + .24 - 0 = .61

 

d) P(A^c) = 1 - P(A) = .63

 

e) P(A^c ∩ B^c) = P(A U B)^c = 1 - P(A U B) = 1 - .61 = .39