a person spins the pointer and is awarded the amount indicated by pointer.It cost $5. to play . There are three sections $2.00 1/2, $5.00 1/4. and $10.00 1/4 what is the expectation of a person who pays. what is the fair price to play game
To calculate the expectation of a person who plays this game, we need to find the average amount of money they can expect to win.
To do this, we'll multiply each possible outcome by its probability and sum them up.
Let's first consider the three sections and their corresponding probabilities:
1. $2.00 with a probability of 1/2
2. $5.00 with a probability of 1/4
3. $10.00 with a probability of 1/4
Now, let's calculate the expectation:
E(X) = ($2.00 * 1/2) + ($5.00 * 1/4) + ($10.00 * 1/4)
E(X) = $1.00 + $1.25 + $2.50
E(X) = $4.75
Therefore, the expectation of a person who pays to play this game is $4.75.
To find the fair price to play the game, we need to determine the maximum amount a person would be willing to pay to play a game that has an average winning of $4.75.
The fair price is typically calculated as 75-80% of the expectation value. Let's take 75% in this case:
Fair price = 0.75 * $4.75
Fair price = $3.56
Hence, the fair price to play this game would be approximately $3.56.