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Zeno is walking on a footpath that will pass an ice-cream stand that is exactly five...

Zeno is walking on a footpath that will pass an ice-cream stand that is exactly five paces along the way. He decides to roll a fair, six-sided die exactly ten times, and to take one pace forward for each time the face of the die is a five or a six. (a) What is probability that Zeno ends up standing in front of the ice-cream stand? (b) Let X be the number of paces that Zeno takes. What is the pmf of X?

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