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$A$ and $B$ throw a pair of dice. If $A$ throws 9 , find $B$ 's chance of throwing a higher number.
Given:
$A$ and $B$ throw a pair of dice. $A$ throws 9.To do:
We have to find $B$ 's chance of throwing a higher number.
Solution:
$\mathrm{A}$ and $\mathrm{B}$ throw a pair of dice.
This implies,
The total number of possible outcomes $n=6\times6=36$.
Outcomes where B throws more than 9 (i.e., 10, 11 and 12) are $(4, 6), (5, 5), (5, 6), (6, 4),(6, 5), (6, 6)$
Total number of favourable outcomes $=6$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability of $B$ 's chance of throwing a higher number $=\frac{6}{36}$
$=\frac{1}{6}$
The probability of $B$ 's chance of throwing a higher number is $\frac{1}{6}$.