survey of 500 people were asked this same question and the results were recorded in a tree diagram in terms of percentages where
M = male, F = female, E = eats breakfast, D = doesn't eat breakfast
11.4.9

a. How many males are in the sample? 

b. How many females are in the sample? 

c. How many males in the sample eat breakfast? 

d. How many females in the sample do not eat breakfast? 

e. What is the probability of selecting a female who doesn't eat breakfast? Round your answer to two decimal places. 

Given the problem involves a tree diagram with percentages and a survey of 500 people, let's approach the problem step-by-step, assuming the typical structure of a tree diagram.

Let's define the percentages based on the data provided:
- \( M = \text{Male} \)
- \( F = \text{Female} \)
- \( E = \text{Eats breakfast} \)
- \( D = \text{Doesn't eat breakfast} \)

To solve the problem, we'll need to use the provided percentages. Since the values seem to be shorthand or incomplete ("11.4.9"), I’ll assume they represent percentages. Here’s a common interpretation:
1. The percentage of males: let's denote as \( x \)%.
2. The percentage of males who eat breakfast and those who don't: let’s assume these are \( y \)% and \( z \)% respectively.
3. The remaining percentages apply similarly to females.

Now, based on typical values of \( x = 50\% \), let’s solve the questions:

### a. How many males are in the sample?

Let’s assume 50% of the sample are males.

\[
\text{Number of males} = 500 \times \frac{50}{100} = 250
\]

### b. How many females are in the sample?

Since the remaining percentage would be females:

\[
\text{Number of females} = 500 - 250 = 250
\]

### c. How many males in the sample eat breakfast?

Assume \( y = 30\% \) of males eat breakfast.

\[
\text{Number of males who eat breakfast} = 250 \times \frac{30}{100} = 75
\]

### d. How many females in the sample do not eat breakfast?

Assume \( z = 20\% \) of females don’t eat breakfast.

\[
\text{Number of females who do not eat breakfast} = 250 \times \frac{20}{100} = 50
\]

### e. What is the probability of selecting a female who doesn't eat breakfast?

\[
P(\text{Female doesn't eat breakfast}) = \frac{\text{Number of females who don't eat breakfast}}{\text{Total number of people}} = \frac{50}{500} = 0.10
\]

Rounding to two decimal places:

\[
P = 0.10
\]

Would you like me to refine values to match the tree diagram, or expand any details? 

**Related Questions:**
1. How do you interpret tree diagrams in probability?
2. What adjustments are needed if percentages differ?
3. How can probability be affected by gender distribution?
4. What if the sample size changes?
5. How to calculate combined events probabilities?

**Tip:** Visualizing data in tree diagrams can simplify probability calculations significantly.

A survey of 500 people were asked this same question and the results were recorded in a tree diagram in terms of percentages where M = male, F = female, E = eats breakfast, D = doesn't eat breakfast. a. How many males are in the sample? b. How many females are in the sample? c. How many males in the sample eat breakfast? d. How many females in the sample do not eat breakfast? e. What is the probability of selecting a female who doesn't eat breakfast? Round your answer to two decimal places.

Explore how to calculate probabilities and percentages using tree diagrams with a sample of 500 people. Learn how to determine the number of males, females, and their breakfast habits, and calculate the probability of selecting a female who doesn't eat breakfast. Ideal for students in Grades 9-12.

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