Suppose you are invited to play a game. A ticket is picked from a box with 10 ti

Question

Suppose you are invited to play a game. A ticket is picked from a box with 10 tickets numbered from one to ten. If you get a 2, 5, 7, you win three dollars. If you get anything else, you lose one dollar. a)How much do you expect to win/lose in 100 games? Find the standard error. b)What is the probability that you win at least $10? c) A fair game is one in which, on average, players neither win nor lose. Change the win-lose dollar amounts in the above game so that it is fair. There are many possible answers. You cannot change the winning numbers 2, 5, 7.

Explanation / Answer

a) In the box, 10 tickets number form 1 to 10.

If you get a 2, 5, 7, you win three dollars. If you get anything else, you lose one dollar.

b) Let X be amount when a game plays one time

E(X) = 3*3/10 - 1*7/10 = 0.2

The expect to win in 100 games = 100*0.2= $20

E(X2) = 32*3/10 + 12*7/10 =3.4

Var(X) = 3.4 - 0.22 = 3.36

Variance to win in 100 games = 100*3.36 = 336

SE = sqrt(336) = 18.33

The probability that you win at least $10 is P(X>=10) = 0.34

d)

Let the winning amount be $7 and loosing amount be $3

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