SOLUTION: 2. A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue.
Algebra.Com
Question 1040480: 2. A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue.
Landing on the blue sector will give 3 points, landing on a yellow sector will give 1 point, landing on a purple sector will give 0 points, and landing on a red sector will give –1 point.
a. Let X = the points you have after one spin. Fill out the missing values in the table.
Xi
P(xi)
b. If you take one spin, what is your expected value?
c. What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue.
A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue.
------------------
Landing on the blue sector will give 3 points, landing on a yellow sector will give 1 point, landing on a purple sector will give 0 points, and landing on a red sector will give –1 point.
a. Let X = the points you have after one spin. Fill out the missing values in the table.
Xi:::...... 3.......1.......0........-1
P(xi)...... 1/7....2/7.....2/7......2/7
------------------------
b. If you take one spin, what is your expected value?
E(Xi) = [3 + 2 + 2 + 2]/7 = 9/7 points = 1.29
--------------------
c. What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values.
-----
Note:: A fair game has an expected value of zero.
There are multiple ways to change Xi and or P(Xi) to achieve that result.
-----
Cheers,
Stan H.
---------------------
RELATED QUESTIONS
A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two... (answered by ikleyn,Edwin McCravy)
A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two... (answered by math_tutor2020)
Suppose that you spin the double wheel pictured to the right. Assuming that the wheels... (answered by jim_thompson5910)
Consider the wheel to the right. If the wheel is spun and each section is equally likely... (answered by Boreal)
Determine the odds against the spinner landing on red. Four out of Eight sectors are red. (answered by stanbon)
how to find the area of... (answered by MathLover1)
1.there are five sectors on a pie chart of which three of them are 25,45 and 90... (answered by addingup)
A dart board has a diameter of 40cm and is divided into 20 congruent sectors. what is the (answered by ikleyn)
In the figure, OAB and OXY are sectors of a circle with centre O. What is the area of the (answered by MathLover1,ikleyn)