Three events A, B and C are defined in the sample space S. The events A and B are mutually exclusive and A and C are independent. What is #P(A|C)#?
# P(A) = 0.2, P(B) = 0.4# and #P(A uu C) = 0.7#
1 Answer
Jan 28, 2017
Explanation:
We use the definition of Conditional Probability;
# P(X | Y) = (P( X nn Y)) / (P(Y))#
Se we have
# P(A | C) = (P( A nn C) ) / (P(C)) #
We are also told that
# :. P(A nn C) = P(A) * P(C) #
So:
# P(A | C) = (P(A) * P(C)) / (P(C)) #
# " " = P(A)#
# " " = 0.2#