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?
