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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?

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thaovtp1407

Answer:

[tex]\frac{1}{6}[/tex]

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) = [tex]\frac{1}{6} *\frac{1}{6}[/tex] = [tex]\frac{1}{36}[/tex]

  • 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* [tex]\frac{1}{6} *\frac{1}{6}[/tex] = [tex]\frac{1}{18}[/tex]

  • 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* [tex]\frac{1}{6} *\frac{1}{6}[/tex] = [tex]\frac{1}{12}[/tex]

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 )

= [tex]\frac{1}{36}[/tex] + [tex]\frac{1}{18}[/tex] + [tex]\frac{1}{12}[/tex] = [tex]\frac{1}{6}[/tex]

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