If you roll two dice, the probability that you roll a sum of 10 is approximately 0.083. What is the probability that you first roll a ten on the 10th roll? What is the average number of rolls until you first roll a 10?

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Answer 1 · 2018-07-11T01:07:55

$Probability = 0.038$

Probability of rolling a 10 = 0.083 so probability of not rolling a 10 $= 1 - 0.083 = 0.917$

So probability of first rolling a 10 on the tenth roll = probability of not rolling a 10 nine times * probability of rolling a 10.

$=0.917*0.917*0.917*0.917*0.917*0.917*0.917*0.917*0.917*0.083$

$= (0.917)^9*0.083$

$= 0.038$