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8. In a box, there are five dimes, two quarters, and three pennies. If a coin is selected at random, what is the probability that it is a quarter or a penny?

A. [tex]\frac{2}{5}[/tex]
B. [tex]\frac{1}{3}[/tex]
C. [tex]\frac{9}{10}[/tex]
D. [tex]\frac{1}{2}[/tex]



Answer :

GinnyAnswer
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].

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