To find the probabilities of selecting a specific type of coin from the jar, we first need to calculate the total number of coins in the jar.
Here’s the breakdown:
- Number of nickels = 70
- Number of dimes = 100
- Number of quarters = 80
- Number of one-dollar coins = 50
Total number of coins:
\[ \text{Total coins} = 70 + 100 + 80 + 50 = 300 \]
Now, we can calculate the probability of selecting each type of coin.
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Probability of selecting a nickel: \[ P(\text{nickel}) = \frac{\text{Number of nickels}}{\text{Total coins}} = \frac{70}{300} = \frac{7}{30} \approx 0.2333 \]
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Probability of selecting a dime: \[ P(\text{dime}) = \frac{\text{Number of dimes}}{\text{Total coins}} = \frac{100}{300} = \frac{1}{3} \approx 0.3333 \]
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Probability of selecting a quarter: \[ P(\text{quarter}) = \frac{\text{Number of quarters}}{\text{Total coins}} = \frac{80}{300} = \frac{8}{30} = \frac{4}{15} \approx 0.2667 \]
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Probability of selecting a one-dollar coin: \[ P(\text{one-dollar coin}) = \frac{\text{Number of one-dollar coins}}{\text{Total coins}} = \frac{50}{300} = \frac{1}{6} \approx 0.1667 \]
Summary of Probabilities:
- Probability of selecting a nickel: \( \frac{7}{30} \) or approximately \( 0.2333 \)
- Probability of selecting a dime: \( \frac{1}{3} \) or approximately \( 0.3333 \)
- Probability of selecting a quarter: \( \frac{4}{15} \) or approximately \( 0.2667 \)
- Probability of selecting a one-dollar coin: \( \frac{1}{6} \) or approximately \( 0.1667 \)