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

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2 only

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Both 1 and 2

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Neither 1 nor 2

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Solution

The correct option is A 1 only
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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Similar questions

If A and B are two mutually exclusive and exhaustive events, then $P (B) = 1 - P (A) .$

If $E_{1}, E_{2}, E_{3} \dots E_{n}$ are n events of a sample space S and if $E_{1} \cup E_{2} \cup E_{3} \cup \dots E_{n} = S$ , then $E_{1}, E_{2} \dots E_{n}$ are called mutually exclusive and exhaustive events.

Q. A sample space S is given as S = {1, 2, 3, 4, 5,6, 7}
Following events are described for this sample space.
Event X = {1,2,3}
Y = {3,4,5}
Z = {5,6}
Events X , Y and Z are exhaustive events.

Q. Assertion :Statement-1 : If A and B be mutually exclusive events in a sample space such that P(A)

= 0.3 a n d P (B) = 0.6,

then

p (¯ A \cap ¯ B) = 0.28

Reason: Statement-2 : If A and B are mutually exclusive events then

P (A \cap B) = 0

Q. A sample space S is given as S = {1, 2, 3, 4, 5,6, 7}
Following events are described for this sample space.
Event X = {1,2,3}
Y = {3,4,5}
Z = {5,6,}
Events X , Y and Z are not exhaustive events because event X and event Y have an element in common

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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?

The correct option is A 1 onlyExhaustive 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.

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?

The correct option is A 1 only
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.