A die is rolled. Let $E$ be the event "die shows $4$ " and $F$ be the event "die shows even number". Are $E$ and $F$ mutually exclusive ?
A die is rolled. Let $E$ be the event "die shows $4$ " and $F$ be the event "die shows even number". Are $E$ and $F$ mutually exclusive ?
When a die is rolled, the sample space is given by
$S =\{1,2,3,4,5,6\}$
Accordingly, $E =\{4\}$ and $F =\{2,4,6\}$
It is observed that $E \cap F=\{4\} \neq \phi$
Therefore, $E$ and $F$ are not mutually exchasive events.
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Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment
$A:$ $^{\prime}$ the sum is even $^{\prime}$.
$B:$ $^{\prime}$the sum is a multiple of $3$$^{\prime}$
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Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment
$A:$ $^{\prime}$ the sum is even $^{\prime}$.
$B:$ $^{\prime}$the sum is a multiple of $3$$^{\prime}$
$C:$ $^{\prime}$the sum is less than $4 $$^{\prime}$
$D:$ $^{\prime}$the sum is greater than $11$$^{\prime}$.
Which pairs of these events are mutually exclusive ?
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- [KVPY 2021]