Math Games

Posts Tagged ‘games place’

Question: Statistics...Math.. can't figure this out?

A fair coin has a “1” on one side and a “2” on the other. A fair four sided die (tetrahedron) is labeled {1,2,3,4}. A coin is flipped and the die is rolled. Let X be the sum of the number face up on the coin and the number we get (call it the side that lands down) on the die.

a.)The probability distribution of X is (exact decimal answers):
2
3
4
5
6

b.)The mean of X is (EXACT decimal place):

c.)The standard deviation of X is (Exactly four places after the decimal) is:

d.)If we generate 5286 such values of X, the sum of all these numbers should be about:

e.)This procedure is turned into a game where the person who flips a coin and rolls a die receives X dollars. If the person who runs the game hopes to make around $85 from 100 players, how much should he charge per game (nearest penny)?

Answer: We can have 8 possibilities:
1,2,3,or 4, plus 1 or 2.
P(2) = 1/8 [1 1]
P(3) = 2/8 [1 2 or 2 1]
P(4) = 2/8 [3 1] or [2 2]
P(5) = 2/8 [4 1] or [3 2]
P(6) = 1/8 [4 2]

The mean is 2 * P(2) + 3 * P(3) + 4 * P(4) + 5 * P(5) + 6 * P(6)
(I got 4, but work it out.)

For question c, use the formula for standard deviation. It's not lending itself to the computer keyboard well.

d) We would expect the mean, multiplied by 5,286.

e) We expect the payout to be $4.00. From 100 players, we want to produce $85 profit. We expect to pay out $400 (mean * 100), so we need to take in $485 from the players. Charge each player $485 / 100, or $4.85.

MATH PARK: BUILD A NUMBER