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Suppose Jane has a fair 5-sided die, and Dick has a fair 8-sided die. Each day, they roll their dice (independently) until someone rolls a

Suppose Jane has a fair 5-sided die, and Dick has a fair 8-sided die. Each day, they roll their dice (independently) until someone rolls a “1”. (Then the person who did not roll a “1” does the dishes.) Find the probability that …

1. a) they roll the first “1” at the same time?

2. a) it takes Dick twice as many attempts as it does Jane to roll the first “1”?

3. a) Dick rolls the first “1” before Jane does?

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