Question

Chris is playing a game with his father with a six-sided die. What is the expected value per roll that Chris will get if his father agrees to give him $2 multiplied by every even number rolled and $1 for every odd number rolled?

Answer 1

$1.50 is the correct answer.

(1/6)(2+2+2+1+1+1) =9/6 =$1.50

Answer 2

Answer:

The the expected value per roll that Chris will get is:

$ 1.5

Step-by-step explanation:

The outcomes on a six-sided cube which are even are:

{2,4,6}

The  outcomes on a six-sided cube which are odd are:

{1,3,5}

Now, we know that the expected value per roll that Chris get from his father is calculated by taking the sum of the product of the price per outcome and the probability of that outcome.

He gets $ 2 for every even number and $ 1 for every odd number.

Now the probability of rolling each number is:

$\dfrac{1}{6}$

Hence, the expected value is given by:

$E(x)=2\times \dfrac{1}{6}+2\times \dfrac{1}{6}+2\times \dfrac{1}{6}+1\times \dfrac{1}{6}+1\times \dfrac{1}{6}+1\times \dfrac{1}{6}\\\\\\E(x)=\dfrac{2+2+2+1+1+1}{6}\\\\\\E(x)=\dfrac{9}{6}\\\\\\E(x)=\dfrac{3}{2}\\\\E(x)=1.5$

               The expected value is:

                            $ 1.5