Expected Value (instruction)~ amdm

For what expected value is a game fair?

E(X)=0

Finding the Expected Value in a Marble Game. Derek and Mia place two green marbles and one yellow marble in a bag. Somebody picks a marble out of the bag without looking and records its color (G for green and Y for yellow). They replace the marble and then pick another marble. If the two marbles picked have the same color, Derek loses 1 point and Mia gains 1 point. If they are different colors, Mia loses 1 point and Derek gains 1 point. What is the expected value of the points for Derek and Mia?

P(GG)= 4/9 P(GY)= 2/9 P(YG)= 2/9 P(YY)= 1/9 For Derek, E(X)= -1/9 For Mia, E(X)= 1/9

Applying the Law of Large Numbers to a Carnival Game At a carnival, you spin a spinner that has four equal-sized sections, each a different color: green, yellow, red, and blue. If you land on green, you win 2 points. If you land on yellow, red, or blue, you lose 1 point. Write the expected value equation. E(V)=1/a(2)+1/b(c)+1/d(e)+1/f(g)

a=4 b=4 c=-1 d=4 e=-1 f=4 g=-1

Setting a Fair Game You pick a card at random from an ordinary deck of 52 cards. If the card is an ace, you get 9 points; if not, you lose 1 point. 4/25 Ace ?/52 Not an ace Write the equation for the expected value. E(V)=4/52(a) + b/52(c)

a=9 b=48 c=-1

The expected value in this case means

after repeated trials of flipping a coin twice, the average number of times heads will turn up is 1.

Suppose you spin the carnival spinner 1,000 times. How many points would you expect to win or lose? -lose 500 points -lose 250 points -win 250 points -win 500 points

lose 250 points

The expected value of the number of points won on a spin is

-0.25

What is the expected value? Should you play the game?

-3/13 points; no, you should not play the game

The expected value for the number of heads is

1

What value for the aces would make the game fair? To find this, solve the equation: 0=4/52(x)+48/52(-1)

12 points

Finding Expected Value How many heads would you expect if you flipped a coin twice? First, fill in the table below with the correct probabilities. Hint: The sample space for flipping a coin twice is {HH, HT, TH, TT}.

A= 1/4 B= 1/2 C= 1/4