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Mutually Exclusive Events

A letter is c...

Question

$A letter is choosen at random from the$
$word 'MATH'. The following are the$
$events associated wth the experiment.$
$E_{1} : Selecting a vowel$
$E_{2} : Selecting a consonant$
$E_{3} : Selecting letters 'A' and 'H'$
$E_{4} : Selecting letters 'M' and 'T'$
$Which of the following pair of$
$events are mutually exclusive$
$events?$

E_{1}, E_{2}

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E_{1}, E_{3}

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E_{2}, E_{4}

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E_{1}, E_{4}

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Solution

The correct options are
A $E_{1}, E_{2}$
D $E_{1}, E_{4}$
Outcomes associated with event $E_{1}$ : A
Outcomes associated with event $E_{2}$ : M, T, H
Outcomes associated with event $E_{3}$ : A, H
Outcomes associated with event $E_{4}$ : M, T

Since, $E_{1}$ and $E_{2}$ have no common outcomes, therefore both these events can not happen together.

Since, $E_{1}$ and $E_{3}$ have 'A' as common outcome, therefore both these events can happen together when selection of 'A' is made.

Since, $E_{2}$ and $E_{4}$ have 'M' and 'T' as common outcomes, therefore both these events can happen together when selection of 'M' and 'T' is made.

Since, $E_{1}$ and $E_{4}$ have no common outcomes, therefore both these events can not happen together.

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Similar questions

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.

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A letter is choosen at random from the word 'MATH'. The following are the events associated wth the experiment. E1:Selecting a vowel E2:Selecting a consonant E3:Selecting letters 'A' and 'H' E4:Selecting letters 'M' and 'T' Which of the following pair of events are mutually exclusive events?