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

Answer:

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,

$\frac{2}{17}$

Probability of getting dime is,

$\frac{3}{17}$

Probability of getting nickel is,

$\frac{3}{17}$

Probability of getting penny is,

$\frac{9}{17}$

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)\times\frac{2}{17}+(0.1)\times\frac{3}{17}+(0.05)\times\frac{3}{17}+(0.01)\times\frac{9}{17}$$=\frac{0.5}{17}+\frac{0.3}{17}+\frac{0.15}{17}+\frac{0.09}{17}$$=\frac{1.04}{17}\approx0.06117\text{ dollars}$