SOLUTION: A certain game consists of rolling a single fair die and pays off as follows: $8 for a 6, $3 for a 5, $1 for a 4, and no payoff otherwise. Find the expected wi
Algebra.Com
Question 1158165: A certain game consists of rolling a single fair die and pays off as follows: $8 for a 6, $3 for a 5, $1 for a 4, and no payoff otherwise. Find the expected winnings for this game.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Answer: $2
==========================================================
Explanation:
Construct a table showing the probabilities of each roll (column 2) and the winnings for each roll (column 1). Column 3 represents the product of columns 1 and 2.
| X | P(X) | W(X) | P(X)*W(X) |
| 1 | 1/6 | 0 | (1/6)*0 = 0 |
| 2 | 1/6 | 0 | (1/6)*0 = 0 |
| 3 | 1/6 | 0 | (1/6)*0 = 0 |
| 4 | 1/6 | 1 | (1/6)*1 = 1/6 |
| 5 | 1/6 | 3 | (1/6)*3 = 3/6 |
| 6 | 1/6 | 8 | 8*(1/6) = 8/6 |
X = roll number selected from set {1,2,3,4,5,6}
P(X) = probability of rolling X
W(X) = winnings for rolling X
Add up the results of column 3 to get:
0+0+0+1/6+3/6+8/6 = (1+3+8)/6 = 12/6 = 2
The expected winnings is $2
RELATED QUESTIONS
PLEASE HELP!
A game consists of rolling a single fair die and pays off as follows: $3... (answered by ewatrrr)
A certain game consists of rolling a single fair die and pays off as follows: $5... (answered by Boreal)
A certain game consists of rolling a single fair die. If a four or five comes up,... (answered by math_helper)
If you play a game that consists of rolling a single fair die and pays off at
$3.00 for... (answered by solver91311)
person pays $2 to play a certain game by rolling a single die once. if a 1 or
2 comes... (answered by Edwin McCravy)
5. In a manufacturing process for ball bearings, the mean diameter is 5mm with a standard (answered by Boreal)
A certain game involves tossing 3 fair coins. It pays 25 cents for 3 heads, 15 cents for... (answered by ikleyn)
A certain game involves tossing 3 fair coins. It pays 29 cents for 3 heads, 12 cents for... (answered by stanbon)
For the experiment of rolling a single fair die, find the probability of obtaining not an (answered by ikleyn)