https://file.aiquickdraw.com/mathbot/file/1726772946358p0mr7bh9.jpg

We are asked to find the probability that exactly one of Jack or Charlie will qualify for the competition.

Looking at the diagram:

- The probability that **Jack qualifies** is \( \frac{3}{10} \), and if Jack qualifies, the probability that **Charlie does not qualify** is \( \frac{7}{8} \).
- The probability that **Jack does not qualify** is \( \frac{7}{10} \), and if Jack does not qualify, the probability that **Charlie qualifies** is \( \frac{1}{8} \).

There are two cases where exactly one of them qualifies:
1. **Jack qualifies** and **Charlie does not qualify**:  
   Probability = \( \frac{3}{10} \times \frac{7}{8} = \frac{21}{80} \)
   
2. **Jack does not qualify** and **Charlie qualifies**:  
   Probability = \( \frac{7}{10} \times \frac{1}{8} = \frac{7}{80} \)

To find the total probability that exactly one qualifies, we add these two probabilities:

\[
\frac{21}{80} + \frac{7}{80} = \frac{28}{80} = \frac{7}{20}
\]

Thus, the probability that exactly one of them qualifies is \( \frac{7}{20} \).

Would you like further details or have any other questions?

Here are 5 questions for further practice:
1. What is the probability that neither Jack nor Charlie qualifies?
2. What is the probability that both Jack and Charlie qualify?
3. If the probability that Charlie qualifies increases, how does that affect the total probability that exactly one of them qualifies?
4. How would the calculation change if Jack's qualification probability was \( \frac{1}{2} \)?
5. What is the complementary probability to the event that exactly one of them qualifies?

**Tip**: Probabilities always sum to 1 across all mutually exclusive outcomes of an event.

What is the probability that exactly one of Jack or Charlie will qualify?

Find the probability that exactly one of Jack or Charlie will qualify in a competition. This problem covers key probability concepts, including the multiplication and addition rules. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation