Question
Probability Invoiving one dle or choosing from n distinct objects A box contains ten cards labeled \( J, K, L, M, N, O, P, Q, R \), and \( S \). One card will be randomly chosen. What is the probability, of choosing a letter from \( L \) to \( Q \) ? Write your answer as a fraction in simplest form.
Ask by Pollard Harper. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The probability of choosing a letter from \( L \) to \( Q \) is \(\dfrac{3}{5}\).
Solution
To determine the probability of choosing a letter from \( L \) to \( Q \) in the box, follow these steps:
1. **List the Total Possible Outcomes:**
The box contains 10 distinct cards labeled: \( J, K, L, M, N, O, P, Q, R, S \).
2. **Identify the Favorable Outcomes:**
The letters from \( L \) to \( Q \) are: \( L, M, N, O, P, Q \). This gives us **6 favorable outcomes**.
3. **Calculate the Probability:**
\[
\text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{6}{10}
\]
4. **Simplify the Fraction:**
\[
\frac{6}{10} = \frac{3}{5}
\]
**Final Answer:**
\(\boxed{\dfrac{3}{5}}\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the probability of choosing a letter from \( L \) to \( Q \), we first identify the letters in that range from the box of cards: \( L, M, N, O, P, Q \). There are 6 letters in total. Next, we know there are 10 cards in total. The probability of drawing one of the favorable letters is calculated by dividing the number of favorable outcomes by the total outcomes: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{6}{10} = \frac{3}{5} \] So, the probability of choosing a letter from \( L \) to \( Q \) is \( \frac{3}{5} \).
