To determine the probability of randomly selecting either a quarter or a penny from a box containing various coins, follow these steps:
1. Count the number of each type of coin:
- Dimes: 5
- Quarters: 2
- Pennies: 3
2. Calculate the total number of coins:
[tex]\[
\text{Total coins} = \text{Number of dimes} + \text{Number of quarters} + \text{Number of pennies}
\][/tex]
[tex]\[
\text{Total coins} = 5 + 2 + 3 = 10
\][/tex]
3. Calculate the probability of selecting a quarter:
The probability of selecting a quarter is the number of quarters divided by the total number of coins.
[tex]\[
P(\text{Quarter}) = \frac{\text{Number of quarters}}{\text{Total coins}} = \frac{2}{10} = 0.2
\][/tex]
4. Calculate the probability of selecting a penny:
The probability of selecting a penny is the number of pennies divided by the total number of coins.
[tex]\[
P(\text{Penny}) = \frac{\text{Number of pennies}}{\text{Total coins}} = \frac{3}{10} = 0.3
\][/tex]
5. Calculate the probability of selecting a quarter or a penny:
Since these are mutually exclusive events (selecting a quarter and selecting a penny cannot happen at the same time), the probability of selecting a quarter or a penny is the sum of the individual probabilities.
[tex]\[
P(\text{Quarter or Penny}) = P(\text{Quarter}) + P(\text{Penny}) = 0.2 + 0.3 = 0.5
\][/tex]
6. Convert the probability back to a fraction:
[tex]\[
P(\text{Quarter or Penny}) = 0.5 = \frac{1}{2}
\][/tex]
Therefore, the probability that a randomly selected coin will be either a quarter or a penny is [tex]\(\frac{1}{2}\)[/tex].
The correct answer is:
(D) [tex]\(\frac{1}{2}\)[/tex].
