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need some help on this question I tried the question out but still don't understand

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closed as off-topic by Saad, Peter Foreman, Jean-Claude Arbaut, Lee David Chung Lin, darij grinberg Apr 23 at 15:39

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The probability of both dice having the same number is $\frac{6}{36}$, as there are $36$ different outcomes, $6$ of which have two of the same number, i.e. $(1,1), (2,2),...$.

The expected number of rolls of this type in $100$ pairs of dice rolls is $100*\frac{6}{36}$

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It is like,

($1$ of grace and $1$ of his friend) or ($2$ of grace and $2$ of his friend) or ($3$ of grace and $3$ of his friend)...........

$\implies (\frac{1}{6} \times \frac{1}{6}) + (\frac{1}{6} \times \frac{1}{6})+(\frac{1}{6} \times \frac{1}{6})+(\frac{1}{6} \times \frac{1}{6})+(\frac{1}{6} \times \frac{1}{6})+(\frac{1}{6} \times \frac{1}{6}) $

$\implies 6 \times \frac{1}{36}$

$\implies \frac{1}{6} $

This means

If they roll $6$ times they get $1$ time the same

So,

If they roll $100$ times they get $\frac{100}{6}$ the same.

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