If there's 38 men and 6 women in group 1, 50 men and 49 women in group 2, 71 men and 29 women in group 3, create the conditional data distribution for each of the groups given that the person was female (round to nearest integer)

To calculate the conditional data distribution for each group given that the person is female, we need to determine the proportion of females in each group as a fraction of the total number of females across all three groups. Here's the step-by-step process:

### Step 1: Total Number of Females
We sum the total number of females across all three groups:
- Group 1: 6 females
- Group 2: 49 females
- Group 3: 29 females

\[
\text{Total Females} = 6 + 49 + 29 = 84
\]

### Step 2: Calculate Conditional Probability for Each Group
For each group, the conditional probability that a person is from that group given that they are female is calculated as:

\[
P(\text{Group } i | \text{Female}) = \frac{\text{Females in Group } i}{\text{Total Females}}
\]

### Step 3: Perform the Calculations

1. **Group 1:**
   \[
   P(\text{Group 1} | \text{Female}) = \frac{6}{84} = 0.071 \quad (\text{Rounded to nearest integer: } 7\%)
   \]

2. **Group 2:**
   \[
   P(\text{Group 2} | \text{Female}) = \frac{49}{84} = 0.583 \quad (\text{Rounded to nearest integer: } 58\%)
   \]

3. **Group 3:**
   \[
   P(\text{Group 3} | \text{Female}) = \frac{29}{84} = 0.345 \quad (\text{Rounded to nearest integer: } 35\%)
   \]

### Step 4: Conditional Data Distribution
The conditional data distribution for each group, given that the person is female, is:

- Group 1: **7%**
- Group 2: **58%**
- Group 3: **35%**

Would you like any more details or have any questions?

Here are 5 related questions you might find interesting:
1. How would the distribution change if we had 10 more women in group 1?
2. What is the total number of people in all three groups?
3. How do we calculate the probability of selecting a female from a random group?
4. How would this problem change if we were looking for the distribution of men instead?
5. How could this data be represented graphically?

**Tip:** Conditional probability depends heavily on the total subset you're considering, so make sure the condition is clearly defined before calculating.

If there's 38 men and 6 women in group 1, 50 men and 49 women in group 2, 71 men and 29 women in group 3, create the conditional data distribution for each of the groups given that the person was female (round to nearest integer).

Explore how to calculate the conditional probability distribution of females across three groups. Learn key concepts like data distribution and conditional probability, with step-by-step calculations for each group. Suitable for students in Grades 9-12.

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