Question

Rolling Dice Roll two standard dice and add the numbers. What is the probability of getting a number larger than 9 for the first time on the third roll?

Answer 1

Answer:

$\frac{1}{6}$

Step-by-step explanation:

The sum is larger than 9, it means we have: 10, 11, and 12

• To get the outcome is 12, we have only one way is that the two dice shows face-6. The probability to have 12 is:

P(12) = $\frac{1}{6} *\frac{1}{6}$ = $\frac{1}{36}$

• To get 11, we have  it two ways once dice shows face-5 and the other shows face-6  and vice versa

P(11) = 2* $\frac{1}{6} *\frac{1}{6}$ = $\frac{1}{18}$

• To get 10, we have it three ways ( once dice shows face-5 and the other shows face-6 and vice versa , two dice show 5)

P(10) = 3* $\frac{1}{6} *\frac{1}{6}$ = $\frac{1}{12}$

So the probability of getting a number larger than 9 for the first time on the third roll is:

P(12) + P(11) +P(10 )

= $\frac{1}{36}$ + $\frac{1}{18}$ + $\frac{1}{12}$ = $\frac{1}{6}$