Question

From the reading, if two probability events A and B are completely exhaustive (sometimes called complementary) then: Question 2 options:

P(A and B) = 0

P(A) + P(B) = 0

P(A or B) = 0

P(A) + P(B) = 1

Answer 1

Ans . P(A) + P(B) = 1

Reason: Theoritical Reasoning

Two or more events are said to be exhaustive if there is a certain chance of occurrence of at least one of them when they are all considered together. There is certainty which means Probability should sum upto 1.

Mathematical Reasoning

These are also called as complementary events.

In other words , if Event A and Event B comprise in the sample space , then Event B is complementary to Event A and vice versa.

We know that ,

P (A) + P(A') = 1

Now since Event A'= Event B

Thus , P(A) + P(B) = 1

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