For the wheel picture on the right assume that a person spins the pointer and is awarded the amount indicated by the pointer. If it costs $5 to play the game determine (a) the expectation of a person who plays the game and (b) the fair price to play the game.

a. what is the expectation? $ ___​

Answer:

(a)

(b)

Step-by-step explanation:

First pic is a second is b

The expectation to play the game is $2.5 and the fair price to play is $7.5.

The expectation is defined as the weighted average value of the random variable which is the product of the value of the random variable and its possibility.

Expectation= ∑P(win)*amount of win or loss of random variable

=∑x*P(x)

Here given that there are only two possible outcomes $5 and $10. And the possibility of every outcome is the same which is 0.5 as they occupy the same area.

As we know

Expectation= ∑P(win)*amount of win or loss of random variable

= 0.5(5-5) +0.5(10-5)

=0.5*0 + 0.5*5

=0+2.5

=$2.5

As fair price= expectation + cost of play

⇒fair price= $2.5 + $5

⇒fair price= $7.5

Therefore the expectation to play the game is $2.5 and the fair price to play is $7.5.

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