Question

Suppose 2 quarters, 3 dimes, 3 nickels, and 9 pennies are in a box. One coin is selected at random. What is the expected value of the money drawn from the box?

Answer 1

Given that,

Suppose 2 quarters, 3 dimes, 3 nickels, and 9 pennies are in a box.

One coin is selected at random.

To find the expected value of the money drawn from the box.

we get,

Total number of coins is 2+3+3+9=17

Probability of getting quarter is,

`(2)/(17)`

Probability of getting dime is,

`(3)/(17)`

Probability of getting nickel is,

`(3)/(17)`

Probability of getting penny is,

`(9)/(17)`

we know that,

`\begin{gathered} 1\text{ quarter}=0.25\text{ dollars} \\ 1\text{ dime}=0.1\text{ dollars} \\ 1\text{ nickel}=0.05\text{ dollars} \\ 1\text{ penny}=0.01\text{ dollars} \end{gathered}`

Using this, we get

The expected value of the money drawn from the box is,

`=(0.25)*(2)/(17)+(0.1)*(3)/(17)+(0.05)*(3)/(17)+(0.01)*(9)/(17)`
`=(0.5)/(17)+(0.3)/(17)+(0.15)/(17)+(0.09)/(17)`
`=(1.04)/(17)\approx0.06117\text{ dollars}`