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,
[tex]\frac{2}{17}[/tex]Probability of getting dime is,
[tex]\frac{3}{17}[/tex]Probability of getting nickel is,
[tex]\frac{3}{17}[/tex]Probability of getting penny is,
[tex]\frac{9}{17}[/tex]we know that,
[tex]\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}[/tex]Using this, we get
The expected value of the money drawn from the box is,
[tex]=(0.25)\times\frac{2}{17}+(0.1)\times\frac{3}{17}+(0.05)\times\frac{3}{17}+(0.01)\times\frac{9}{17}[/tex][tex]=\frac{0.5}{17}+\frac{0.3}{17}+\frac{0.15}{17}+\frac{0.09}{17}[/tex][tex]=\frac{1.04}{17}\approx0.06117\text{ dollars}[/tex]