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Mathematical Expectation
You're playing basketball toss at an amusement park. To play, you pay 50 cents and shoot three balls (no refunds). Make one basket, you get a 5 cent key chain, two wins you a stuffed animal worth 60 cents, and three wins you a doll worth $2.50. The probability of making a basket is 30%. What is the mathematical expectation for the game? How do you interpret the answer?
Equation
E= (-50 + 10 -50 + 10 -50 +100)/6
= 3(-50) + 2(10) + 1(100)
6
=3/6(-50) + 2/6(10) + 1/6(100)
These are the payoffs of each number. You can calculate the mathematical expectation of a random event by multiplying the probability and the value for each mutually exclusive event and then adding the results.
E=P(A1)a1+ P(A2)a2+ P(A2)a2+…+ P(An)an
E is mathematical expectation (the sum)
Definition
At a carnival, students are awarded points for playing game. At the end of the evening, they can trade their points for prizes. For a particular game, students pay 50pts to roll a die. The payoffs for the game are:
- Roll a 6: win 100pts (and keep your 50pts)
- Roll a 2 or a 4: win 10pts (and keep your 50pts)
- Roll an odd number: Win nothing (and lose your 50pts
If you roll each number one time in six rolls (assuming each number is equally likely to appear) your total winnings would be -30pts. Your average would be -5pts per roll
The weighted average of the values for a random experiment each time it is run. The "weights" are the probabilities of each outcome
P(0)= 3C0* 0.7^3* 0.3^0= 0.343
P(1)= 3C1* 0.7^2* 0.3^1= 0.411
P(2)= 3C2* 0.7^1* 0.3^2= 0.189
P(3)= 3C3* 0.7^0* 0.3^3= 0.027
Total= 1.000