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Select the correct answer from each drop-down menu.

\begin{tabular}{|l|c|c|c|c|}
\hline
\multirow{2}{*}{ Hemoglobin Level } & \multicolumn{4}{|c|}{ Age } \\
\cline { 2 - 5 } & Less than 25 Years & 25-35 Years & Above 35 Years & Total \\
\hline Less than 9 & 21 & 32 & 76 & 129 \\
\hline Between 9 and 11 & 49 & 52 & 46 & 147 \\
\hline Above 11 & 69 & 44 & 40 & 153 \\
\hline Total & 139 & 128 & 162 & 429 \\
\hline
\end{tabular}

Based on the data in the two-way table, answer the following:

1. The probability of being [tex]$25-35$[/tex] years old given a hemoglobin level above 11 is [tex]$\square$[/tex].
2. The probability of being [tex]$25-35$[/tex] years old is [tex]$\square$[/tex].
3. Being 25-35 years old and having a hemoglobin level above 11 are [tex]$\square$[/tex] dependent on each other.

Sagot :

GinnyAnsweridn
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.
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