A game is played where a biased coin is flipped. A head is twice as likely as a tail. It costs $5 to plat the game and if a head occurs you win &7 but if a tail occurs you pay $3 which of the following is correct?

Question

The game is fair
The expected valve of net gain is positive and the player should play.

The expected valve of net gain is negative and the player should play

The expected valve of net gain is positive and the player should not play

The expected valve of net gain is negative and the player should not play

Answer 1

prob of tail --- x
prob of head --- 2x

x+2x = 1
3x=1
x = 1/3

expected win = (1/3)7 + (2/3)(-3) = 1/3 or $.33
but you are paying $5.00 for a return of .33, silly!

"The expected valve of net gain is positive and the player should not play "

Answer 2

A student is interested in earning some money to pay her tuition. A game is proposed that is very enticing. Roll two dice; pay $25 to play if a sum of 10 or larger occurs she pays $8; if a sum of 3 or smaller occurs she pays the amount of sum in dollars; if another sum occurs she earns the value of the sum in dollars

Which statement is correct ?

The game is fair

The expected valve of net gain is positive and player should play

The expected valve of net gain is negative and the player should play

The expected valve of net gain is positive and the player should not play

The expected valve of net gain is negative and the player should not play

Answer 3

Price to play the game = $25
Sum/return
2/2
3/3
4/4
5/5
6/6
7/7
8/8
9/9
10/8
11/8
12/8
So the maximum return is $9 (if she throws a sum of 9), can never recover the $25 she pays to play.
If she is the player, the recommendation is:
"The expected valve of net gain is negative and the player should not play"

She might make some money for college if she organizes the game.