Given:
A jar of coins has 8 pennies, 5 nickels, 1 dime, and 7 quarters.
To find:
The probability of drawing a quarter, replacing it, and drawing another quarter.
Solution:
A jar of coins has 8 pennies, 5 nickels, 1 dime, and 7 quarters.
Total number of coins = 8+5+1+7 = 21
Probability of getting a quarter is
[tex]P(Quarter)=\dfrac{\text{Number of quarters}}{\text{Total number of coins}}[/tex]
[tex]P(Quarter)=\dfrac{7}{21}[/tex]
[tex]P(Quarter)=\dfrac{1}{3}[/tex]
After drawing a quarter, we replaced it. So, the probability of getting quarter in second draw is the same and first one, .i.e., [tex]P(Quarter)=\dfrac{1}{3}[/tex].
The probability of drawing a quarter, replacing it, and drawing another quarter is
[tex]P=\dfrac{1}{3}\times \dfrac{1}{3}[/tex]
[tex]P=\dfrac{1}{9}[/tex]
Therefore, the required probability is [tex]\dfrac{1}{9}[/tex].
