# 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#