$A$ 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 $\frac{1}{6}$.      

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Updated on: 10-Oct-2022

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