If P(A) = 2/3, P(B) = 3/5, P(A U B) = 5/6 then P(A/B’) is:
(a) 7/12 (b) 5/12
(c) 1/4 (d) ½
Answers
Therefore the required Probability of occurrence of A given that B does not happen P(A/B’) is 7/12. ( Option - a )
Given:
Probability of event A occurs = P(A) = 2/3
Probability of event B occurs =P(B) = 3/5
Probability of any one of the events either A and B occurs=P(A U B) = 5/6
To Find:
Probability of occurrence of A given that B does not happen.
Solution:
This numerical can be simply solved as shown below.
Given that:
P(A) = 2/3, P(B) = 3/5, P(A U B) = 5/6
Probability of event B does not happen = P ( B¹ ) = 1 - P ( B ) = 1 - 3/5 = 2/5
Probability of both the events A and B occurs = P ( A ∩ B ) is given by
P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B )
⇒ 5/6 = 2/3 + 3/5 - P ( A ∩ B )
⇒ 5/6 = 19/15 - P ( A ∩ B )
⇒ P ( A ∩ B ) = 13/30
Now P ( A ∩ B¹ ) = P ( A ) - P ( A ∩ B )
⇒ P ( A ∩ B¹ ) = 2/3 - 13/30 = 7/30
Finally, P ( A/B¹ ) = P ( A ∩ B¹ ) / P ( B¹ )
⇒ P ( A/B¹ ) = ( 7/30 ) / ( 2/5 ) = ( 7 × 5 ) / ( 30 × 2 ) = 7/12
Therefore the required Probability of occurrence of A given that B does not happen P(A/B’) is 7/12.