SOLUTION: It is known that P(A)=0.3, P(B)=0.6, P(A and B')= 0.1. Find the probability of P( A U B)

Algebra ->  Probability-and-statistics -> SOLUTION: It is known that P(A)=0.3, P(B)=0.6, P(A and B')= 0.1. Find the probability of P( A U B)      Log On


   

Question 1095453: It is known that P(A)=0.3, P(B)=0.6, P(A and B')= 0.1. Find the probability of P( A U B)
Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!

Let x,y,z, and w be the probabilities of the 4 regions
in the Venn diagram below:



P(A) = x+y = 0.3
P(B) = y+z = 0.6
P(A&B') = x = 0.1
P(AUB) = x+y+z = ??

Since x = 0.1,

substitute 0.1 for x in x+y = 0.3
                      0.1+y = 0.3
                          y = 0.2

Substitute 0.2 for y in y+z = 0.6
                      0.2+z = 0.6
                          z = 0.4

 P(AUB) = x+y+z = 0.1+0.2+0.4 = 0.7   <--answer

It's also true that w = P(A'&B') = 1 - 0.7 = 0.3




Edwin