If two events A and B are such that, P(A')=0.3,P(B)=0.4,P(A∩B')=0.5, then PB(AUB') is equal to
12
13
14
None of these
Explanation for the correct answer:
Finding the value of PB(AUB'):
Given that,
P(A')=0.3,P(B)=0.4,P(A∩B')=0.5PA=1-P(A')=0.7PB'=1-P(B)=0.6
We know,
PAB=PA∩BPB
So,
PB(AUB')=[P(B∩(AUB')]P(AUB')
The above equation can be written as
PB(AUB’)=PA∩B[PA+PB'-PA∩B']=[P(A)-P(A∩B')][P(A)+P(B')-P(A∩B')]
Now, substitute the values, and we get
PB(AUB')=[0.7-0.5][0.7+0.6-0.5]=0.20.8=28=14
Hence, the correct option is C.