Question

John and Lucy take turns rolling two dice. If John rolls a pair larger than or equal to 10 he wins and the game stops. If Lucy rolls a pair strictly smaller than 10, she wins and the game stops. They keep rolling in turn until one of them wins. Suppose John rolls first. What is the probability that Lucy wins

Answer 1

56.25%

Explanation:

If John rolls first and Lucy rolls second, in order to find the probability that Lucy wins we need to multiply the probability that John's roll is less than 10 by the probability that Lucy's roll is less than 10. There are a total of 12 possible outcomes that can occur in a pair of dice, therefore John's probability of rolling less than a 10 would be
`(9)/(12)` which would also be the same probability of Lucy rolling smaller than a 10. Now we simply multiply this probability by itself...

`(9)/(12) * (9)/(12) = (81)/(144)` or 0.5625

We can multiply this decimal by 100 to get the percentage probability

0.5625 * 100 = 56.25%

The probability of Lucy winning the game is 56.25%