Question

In: Statistics and Probability

4.Consider events A and B, neither of which are impossible events. Prove the following statements. A)(4...

4.Consider events A and B, neither of which are impossible events. Prove the following

statements.

A)? ? ? = 1 − ?(?|?)

B)If ? ? ? ? = ? ? ∩ ? , then A and B must be independent events.

Expert Solution

Question 4

Two events are A and B, neither of which are impossible events.

Question (A)

We have to prove

Now, we see

By definition of conditional probability,

Hence Proved.

Question (B)

If A and B are independent events, it means that the occurrence of A is independent of the occurrence of B.

In probability terms, it means

Now, it is given

By definition of conditional probability, this becomes

Hence proved, A and B must be independent.

orchestra answered 3 years ago

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