# Imp 1 Pow What's on Back

Problem Statement

In this problem I am looking at strategies for a game called What’s on Back? This game has 3 cards. One card has an X on both sides, one card has an O on both sides, and one has an O on one side and a X on the other. On your turn you choose one of the cards at random from a bag. You hold it up with one side facing you. You are not allowed to look at the other side or the other cards. You have to predict whether it is an O or an X on the other side of the card. My task is to look at a bunch of different strategies for playing and find the probability of success for each one. For each strategy I look at I have to find the probability using both an experimental and theoretical model. My real goal is to find the strategy with the highest probability of success or the one most likely to help me win.

Strategy # 1

a. Always choose the same thing the card says. So if it is an O choose O, if it is an X choose X. b. 30 trials

1. yes 6.no 11.no 16.yes 21.yes 26. yes 2. yes 7.yes 12.yes 17.yes 22.no 27. yes 3. yes 8.no 13.yes 18.no 23.yes 28. yes 4. no 9.no 14.yes 19.yes 24.no 29. yes 5.no 10.yes 15.yes 20.no 25.no 30. Yes

P (right) – 18/30 or 6/10 or .6

Success rate = .6

c. (XX)-works-1/6

(XX)-works-1/6

(OO)-works-1/6

(OO)-works-1/6

(OX)-doesn’t work

(XO)-doesn’t work total successful – 4/6 or 2/3 or .66 Success rate = .66

Strategy #2

a. Always choose O no matter what.

b. 30 trials

1. yes 6.no 11.yes 16.yes 21.no 26.yes

2. yes 7.no 12.yes 17.yes 22.no 27.no

3. no 8.yes 13.no 18.yes 23.no 28.yes

4. no 9.no 14.yes 19.yes 24.yes 29.yes

5.no 10.yes 15.yes 20.yes 25.no 30.no

P (right) – 17/30 or .56

Success rate = .56

c. (XX)-doesn’t work

(XX)-doesn’t work

(OX)-doesn’t work...

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