If A and B are two independent events such that P(A)=12,P(B)=15,then
P(A/B)=1/2
P(A/AUB)=5/6
P(A∩B/A'UB')=0
All of these
Step 1. Find the value of P(AB):
Given, P(A)=12
P(B)=15
We know that, P(AB) = P(A∩B)P(B)
= PA·PBPB [∵PA∩B=PA·P(B)]
= PA
∴ PAB = 12
Step 2. Find the value of P(A/AUB):
We know that, P(A/AUB) = P(A∩(AUB))/P(AUB)
= PA/PAUB ....1 [∵PA∩(AUB)=PA]
As P(AUB) = P(A)+ P(B)- P(A∩B)
=12+15-1215 [∵PA∩B=PA·P(B)]
= 610
∴ PAUB = 35
Therefore, equation 1 becomes
P(A/AUB) = 1235
∴ P(A/AUB) = 56
Step 3. Find the value ofP(A∩B/A'UB')
P(A∩B/A'UB') = P(A∩B)∩P(A'UB')P(A'UB')
∴ P(A∩B/A'UB') = 0
Hence, option "D" is correct.
If A and B are two events such that P(A)=12, and P(B)=23, then
If A and B are two events such that P(AUB)=56, P(A∩B)=13, and P(B')=13, then P(A)=?
If A and B are two events such that P(A)=38, P(B)=58, and P(AUB)=34, then P(A/B)=?
Arrange 12,13,34, 56 in ascending order.
If A and B are two events of a random experiment, such that PA∪B=45,PA'∪B'=710, and P(B)=25, then the value of P(A) equals