Question

Select all expressions that are equivalent to the specified probability using the given independence assumptions. Given no independence assumptions, P(A,B∣C)= Given that A is independent of B given C,P(A,B∣C)= Given no independence assumptions, P(A∣B,C)= Given that A is independent of B given C,P(A∣B,C)=

Answer 1

The expressions equivalent to the specified probabilities with the given independence assumptions are determined using the product rule and the independence of events.

Step-by-step explanation:

Given the independence assumptions, we can determine the equivalence of the specified probabilities:

P(A,B|C) = P(A|C) * P(B|C) - This is the product rule for independent events. If A and B are independent given C, then the probability of A and B occurring given C is the product of the individual probabilities.

P(A,B|C) = P(A|C) * P(B|C) = P(A|C)

P(A|B,C) = P(A|C) - If A is independent of B given C, then the probability of A given B and C is the same as the probability of A given C.

P(A|B,C) = P(A|C)