Suppose that P(A) = 0.3 and P(B) = 0.25 and P(A ∩ B) = 0.1. What is P(B | A(complement))?
1 Answer
Feb 24, 2017
Explanation:
We use the definition of conditional probability:
# P(X|Y) = (P(X nn Y)) / (P(Y)) #
along with
# P(X nn Y') = P(X) - p(X nn Y) #
From this we get;
# P(B|A') = (P( B nn A')) / (P(A')) #
And
# P(B nn A') = P(B) - P(B nn A) #
We are given that
# P(A) \ \ \ \ \ \ \ \ \ \=0.3 => P(A')=0.7 #
# P( B nn A') = 0.25 - 0.1 = 0.15 #
Hence;
# P(B|A') = 0.15 /0.3 = 0.5 #