Consider the following statements :(1) If A and B are exhaustive events, then their union is the sample space.(2) If A and B are exhaustive events, then their intersection must be an empty event.Which of the above statements is/are correct?

Engineering

Mathematics

Basic Definitions Related to Probability

Question

Consider the following statements :

(1) If A and B are exhaustive events, then their union is the sample space.

(2) If A and B are exhaustive events, then their intersection must be an empty event.

Which of the above statements is/are correct?

1 only

2 only

Both 1 and 2

Neither 1 nor 2

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Exhaustive events are those events, whose union covers the whole sample space. The probability of occurring at least one of them is 1. So, their intersection may or may not be empty.

Hence, A is correct.

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