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∣C)?

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

1 Answer
Steve M
Jan 28, 2017

P(A | C) = 0.2 P(A∣C)=0.2

Explanation:

We use the definition of Conditional Probability;

P(X | Y) = (P( X nn Y)) / (P(Y))P(X∣Y)=P(X∩Y)P(Y)

Se we have

P(A | C) = (P( A nn C) ) / (P(C)) P(A∣C)=P(A∩C)P(C)

We are also told that AA and CC 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

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