Question

A certain game consists of rolling a single fair die and pays off as follows: $10 for a 6, $7 for a 5, $4 for a 4, and no payoff otherwise,Find the expected winnings for this game.The expected winnings for this game are ?(Round to the nearest hundredth.)Enter your answer in the answer box,

Answer 1

Answer:

$3.50

Explanation:

In a standard die, the total number of possible outcomes = 6.

$\begin{gathered} P(\text{obtaining a 6)=}\frac{1}{6} \\ P(\text{obtaining a 5)=}\frac{1}{6} \\ P(\text{obtaining a 4)=}\frac{1}{6} \\ P(\text{obtaining a 1,2 or 3)=}\frac{3}{6} \end{gathered}$

To find the expected winnings, multiply each payoff by its probability and sum it up:

$\begin{gathered} \text{Expected Winnings=}(P(\text{others)x}0)+(P(\text{4)x4})+(P(5\text{)x7})+(P(6\text{)x10}) \\ =(\frac{3}{6}\times0)+(\frac{1}{6}\times4)+(\frac{1}{6}\times7)+(\frac{1}{6}\times10) \end{gathered}$

Simplify:

$\begin{gathered} =0+\frac{2}{3}+\frac{7}{6}+\frac{10}{6} \\ \approx\ 3.50 \end{gathered}$

The expected winnings for this game are $3.50 (to the nearest hundredth).