Question

Amanda is playing a game of chance in which she rolls a number cube with sides numbered from to 1 to 6. The number cube is fair, so a side is rolled at random. This game is this: Amanda rolls the number cube once. She wins $1 if a 1 is rolled, $2 if a 2 is rolled, $3 if a 3 is rolled, and 4 if a 4 is rolled. She loses $0,50 if a 4, 5 or 6 is rolled.

(a) Find the expected value of playing the game.
(b) What can Elsa expect in the long run, after playing the game many times?
1) Elsa can expect to gain money. She can expect to win__dollars per roll.
2) Elsa can expect to lose money. She can expect to lose___dollars per roll.
3) Elsa can expect to break even (neither gain nor lose money).

Answer 1

a. 0.75

b. elsa can expect to gain money. 0.75$

Step-by-step explanation:

x = 1/6 = 0.166667

given an outcome of 1,

1$ win * 0.166667 = 0.166667

given an outcome of 2,

$2 win * 0.166667 = 0.33333

given an outcome of 3,

$3 win*0.166667 = 0.5

remember that if she has an out come of 4, 5 and 6 she loses 0.5 dollars

given an outcome of 4,

-$0.5 * 0.166667 = -0.083333

given an outcome of 5,

-$0.5 * 0.166667 = -0.083333

given an outcome of 6,

-$0.5 * 0.166667 = -0.083333

The expected value of playing the game = 0.166667+0.333333+0.5-0.083333-0.083333-0.083333

= 0.750001

expected value of plying game = 0.75

b. in the long run, after playing the game many times, Elsa can expect to gain money. she can expect to win 0.75$ per role. option 1