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Question

A series with three matches between India and South Africa is about to start. Consider the three events associated with the result of the match.
A. SA wins at least two matches
B. SA wins exactly one match
C. SA wins no match

Statement: The three events A, B and C are mutually exclusive and exhaustive events.


A

True

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B

False

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Solution

The correct option is A

True


Two events are said to be mutually exclusive if there is no common element in both or AB=ϕ.

A set of events E1,E2,E3.....En are said to be exhaustive, if E1E2E3En=S. (sample space)

Let us find out the sample space by denoting South Africa winning as S and India winning as I.

S = {SSS, SSI, SIS, ISS, SII, ISI, IIS, III}

There are eight elements in the sample space S.

Now let's find out the events A, B and C

Event A

A is defined as SA wins at least two matches. From the sample space we can see that there are 4 elements with at least two SA wins in it.

A = {SSS, SSI, SIS, ISS}

Event B

SA wins exactly one match

B = {SII, ISI, IIS}

Event C

SA wins no match

C = {III}

Now let's check if the given events A, B and C are mutually exclusive and exhaustive.

AB=ϕ,BC=ϕ,CA=ϕ

A, B and C are mutually exclusive

ABC = {SSS, SSI, SIS, ISS, SII, ISI, IIS, III}

= Sample space

Exhaustive

Mutually exclusive and exhaustive.


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