Question

Find the chance of getting a sum of $9$ at least twice in $10$ throws with $2$ dice.

Answer 1

Total possible outcomes=6$\times$6=36

For sum to be 9 possible outcomes are(3,6)(4,5)(5,4)(6,3)

In 10 throw of dice probability of getting sum 9 at least twice

=1- P(no 9)-P(one 9)

=1 - $\frac{{{32}_C}_2}{{{36}_C}_2}$-$\frac{{{32}_C}_1\times {4_C}_1}{{{36}_C}_2}$

=140/1260=0.1111