Question
2. Ms. Mitchells' coin purse has 20 coins. There are 6 pennies, 4 quarters, 3 dimes, and the remainder are nickels. What is the theoretical probability of randomly selecting a nickel from Ms. Mitchells' coin purse?
Ask by Howell Summers. in the United States
Jan 29,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The probability of selecting a nickel is 7 out of 20, which is 35%.
Solution
To determine the theoretical probability of randomly selecting a nickel from Ms. Mitchell's coin purse, follow these steps:
1. **Total Number of Coins:**
- Ms. Mitchell has a total of **20 coins**.
2. **Breakdown of the Coins:**
- **Pennies:** 6
- **Quarters:** 4
- **Dimes:** 3
- **Nickels:** To find the number of nickels, subtract the total number of pennies, quarters, and dimes from the total number of coins:
\[
\text{Number of nickels} = 20 - (6 + 4 + 3) = 20 - 13 = 7
\]
3. **Calculating the Probability:**
- **Probability (P) of selecting a nickel** is the ratio of the number of nickels to the total number of coins:
\[
P(\text{nickel}) = \frac{\text{Number of nickels}}{\text{Total number of coins}} = \frac{7}{20}
\]
- This can also be expressed as **35%** if you prefer a percentage.
**Final Answer:**
The probability of selecting a nickel is \(\frac{7}{20}\) or 35 %.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find the number of nickels, we first calculate how many coins are not nickels: 6 (pennies) + 4 (quarters) + 3 (dimes) = 13 coins. Therefore, there are 20 - 13 = 7 nickels. The theoretical probability of randomly selecting a nickel is the number of nickels divided by the total number of coins: P(nickel) = 7/20. This means there’s a 35% chance you'll pull out a nickel from Ms. Mitchell's purse when you plunge your hand in there. Quite the treasure trove of coins to sift through! Remember, probabilities can guide us, but each coin toss is still a lucky dip!
