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)#?

Question

# P(A) = 0.2, P(B) = 0.4# and #P(A uu C) = 0.7#

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Answer 1 · 2017-01-28T00:35:11

# P(A | C) = 0.2 #

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 #A# and #C# are independent events

# :. P(A nn C) = P(A) * P(C) #

So:

# P(A | C) = (P(A) * P(C)) / (P(C)) #
# " " = P(A)#
# " " = 0.2#