To determine the required probabilities and dependence, let's break down the parts step-by-step based on the given data in the table.
### Step 1: Determine the Probability of Being 25-35 Years Old Given a Hemoglobin Level Above 11
We need to find the conditional probability of being 25-35 years old given that the hemoglobin level is above 11. This means we will focus only on the row where the hemoglobin level is "Above 11."
From the table:
- Number of individuals aged 25-35 with a hemoglobin level above 11: 44
- Total number of individuals with a hemoglobin level above 11: 153
So, the conditional probability is computed as:
[tex]\[ P(\text{25-35}|\text{Above 11}) = \frac{44}{153} \approx 0.2876 \][/tex]
### Step 2: Determine the Probability of Being 25-35 Years Old in General
To find the general probability of being in the age range of 25-35 years, we consider the total number of individuals in that age range divided by the total population.
From the table:
- Total number of individuals aged 25-35: 128
- Total population: 429
So, the general probability is:
[tex]\[ P(\text{25-35}) = \frac{128}{429} \approx 0.2984 \][/tex]
### Step 3: Determine Dependency
We need to check if being 25-35 years old and having a hemoglobin level above 11 are dependent events. For this, we compare the conditional probability [tex]\( P(\text{25-35}|\text{Above 11}) \)[/tex] with the general probability [tex]\( P(\text{25-35}) \)[/tex].
Since:
[tex]\[ P(\text{25-35}|\text{Above 11}) \approx 0.2876 \][/tex]
[tex]\[ P(\text{25-35}) \approx 0.2984 \][/tex]
There is a difference between these probabilities, which suggests that the events are dependent. Thus, being 25-35 years old and having a hemoglobin level above 11 are dependent on each other.
To summarize, we get:
- The probability of being 25-35 years old given a hemoglobin level above 11 is approximately 0.2876.
- The probability of being 25-35 years old in general is approximately 0.2984.
- Being 25-35 years old and having a hemoglobin level above 11 are dependent on each other.
So, the correct answers for the drop-down menus would be:
- The probability of being [tex]$25-35$[/tex] years old given a hemoglobin level above 11 is 0.2876.
- The probability of being [tex]$25-35$[/tex] years old is 0.2984.
- Being 25-35 years old and having a hemoglobin level above 11 are dependent on each other.
