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Sally plays a game and wins with probability p. Every week, she plays until she wins...

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Statistics

Sally plays a game and wins with probability p. Every week, sheplays until she wins two games, and then stops for the week. Sallycalls it a \"lucky week\" if she manages to achieve her goal in 7 orless games.

a) If p = 0.2, what's the probability that Sally will have a\"lucky week\" next week?

b) What's the probability of exactly 3 \"lucky weeks\" in the next5 weeks? What's the expected number of \"lucky weeks\" Sally willhave in the next 10 weeks?

c) Let X be the number of games Sally plays in a week, and let q= 1 – p. Find the expectation E[X].

d) If Sally pays $1 to play each game, and gets $5 for each gameshe wins, what's her expected earning at the end of each week?

Answer & Explanation Solved by verified expert
3.7 Ratings (713 Votes)
a Sally achieve in 2 games P X 2 C22 022 1020 0040 Sally achieve in 3 games P X 2 C21 021 1021 02 0064 Sally achieve in 4    See Answer
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