Question

suppose 7 quarters, 6 dimes, 3 nickels, and 8 pennies are in a box. one coin is selected at random. What is the expected value of the money drawn from the box? ____ cents. (round to the nearest tenth as needed).

Answer 1

`\begin{gathered} \text{ First step, find the probability of each coin.} \\ \text{ Since there are 24 coins in total (7 quarters, 6 dimes, 3 nickels and 8 pennies)} \\ \text{ The probability is } \\ 25c\rightarrow(7)/(24) \\ 10c\rightarrow(6)/(24) \\ 5c\rightarrow(3)/(24) \\ 1c\rightarrow(8)/(24) \\ \text{ To get the expected value, multiply the probability of each coin to their respective} \\ \text{value},\text{ and add them all together} \\ E(X)=25c\cdot(7)/(24)+10c\cdot(6)/(24)+5c\cdot(3)/(24)+1c\cdot(8)/(24) \\ E(X)=(175)/(24)+(5)/(2)+(5)/(8)+(1)/(3) \\ E(X)=(43)/(4)\rightarrow10.75c \\ 10.75\text{ cents rounded to the nearest tenth is 10.8 cents} \\ \text{Therefore, the expected value of 10.8 cents.} \end{gathered}`