Question

Sally plays a game and wins with probability p. Every week, she plays until she wins two games, and then stops for the week. Sally calls it a "lucky week" if she manages to achieve her goal in 7 or less 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 next 5 weeks? What's the expected number of "lucky weeks" Sally will have 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 game she wins, what's her expected earning at the end of each week?

Answer 1

Answer d:

If Sally is expected to play 10 games ,

and she pays $1 and gets $5 for each game she wins , then the

expected earning at the end of each week is $(50 - 10) = $40

All Answers -

• a. The required probability is 0.4232
• b. expected number of "lucky weeks" is 4.232
• c. Expected number of games played = 10
• d. Expected earning is $40