Let A, B and C be independent events. Show that: P(A ∪ B|C) = P(A|C)P(B|C) When this condition is satisfied, A and B are said to be conditionally independent events given the event C.
Let A, B and C be independent events. Show that:
P(A ∪ B|C) = P(A|C)P(B|C)
When this condition is satisfied, A and B are said to be conditionally independent events given the
It seems that the problem is incorrect. It should be P(A B|C) = P(A|C)P(B|C) instead of P(A ∪ B|C) = P(A|C)P(B|C). We will assume this as a typo and proceed with this problem.
A number of events are considered to be independent if the probability of occurrence of any one of them is not affected by the occurrence of any number of the remaining events. And when one event depends on the occurrence of the other event, we use conditional probability. It is the probability of the second event assuming that the first event has already been occurred.
Step by step
Solved in 2 steps
