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 $1.00.

a) Describe the box model for this game.---?---

b) How much do you expect to win/lose in 100 games? ---?--- Find the standard error. ---?---

c) What is the probability that you win at least $10? ---?---

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

X (amount) 3 1

P(X=x) 3/10 7/10

E(X) = 3*3/10 - 1*7/10 = 8/10 = 0.8

The expect to win in 100 games = 100*0.8 = $80

E(X2) = 32*3/10 - 12*7/10 = 2

Var(X) = 2 - 0.82 = 1.36

Variance to win in 100 games = 100 * 1.36 = 136

SE = sqrt(136) = 11.66

b)   The probability that you win at least $10 is P(X>=10) = P(Z> (10 - 80 /11.66)

=P(Z> 6.0) = approx 1

c) the game will be fair if E(X) = 0

Let X be amount when a game plays one time

X (amount) x -x

P(X=x) 3/10 7/10

Given E(X) = 0

a *3/10 - b *7/10 = 0

3a - 7b = 0

a = 7b/3

There are many answers as 'a' and 'b' can be any numbers.

One set is:

b = 3 and a = 7

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