Question

the expected value is $1.71 . If the same bet is made 872 times ,how much would you expect to win or lose? round your answer to two decimal places .Losses must be expressed as negative value

Answer 1

cardsWe were given the following information:

A standard deck of cards has 52 cards

There are 13 Clubs cards in a standard deck

The probability of drawing a Clubs card is given by:

`P_1=(13)/(52)`

In the second draw, there are 51 cards left. The probability of picking a Clubs is given by:

`P_2=(12)/(51)`

The total probability is equal to the product of the individual probabilities, this is:

`\begin{gathered} P=P_1* P_2 \\ P=(13)/(52)*(12)/(51) \\ P=0.0588\approx0.059 \\ P=0.059 \end{gathered}`

The Expected Value for 1 game is calculated as shown below:

`\begin{gathered} EV=P_1*X_1+P_2*X_2 \\ X_1=\text{event of }winning\text{ \$}765,P_1=0.059 \\ X_2=\text{event of }losing\text{ \$}46,P_2=1-0.059=0.941 \\ EV=(0.059*765)-(0.941*46) \\ EV=45.135-43.286 \\ EV=1.849\approx1.85 \\ \\ \therefore EV=\text{\$}1.85 \end{gathered}`

If the same bet is done 872 times, I would expect to win:

`\begin{gathered} 872\cdot EV=872*1.85 \\ 872\cdot EV=1613.20 \end{gathered}`

I would expect to win $1,613.20