To address the provided question, we need to calculate the probability of side effects for both adults and children and then compare these probabilities. We will base our calculations on the given table:
[tex]\[
\begin{array}{|l|c|c|c|}
\hline
& \text{Side effects} & \text{No side effects} & \text{Total} \\
\hline
\text{Adults} & 6 & 44 & 50 \\
\hline
\text{Children} & 20 & 30 & 50 \\
\hline
\text{Total} & 26 & 74 & 100 \\
\hline
\end{array}
\][/tex]
### Step-by-Step Solution:
1. Calculate the probability that an adult has side effects:
[tex]\[ P(\text{side effects} \mid \text{adult}) = \frac{\text{Number of adults with side effects}}{\text{Total number of adults}} \][/tex]
From the table, the number of adults with side effects is 6, and the total number of adults is 50. Therefore:
[tex]\[ P(\text{side effects} \mid \text{adult}) = \frac{6}{50} = 0.12 \][/tex]
2. Calculate the probability that a child has side effects:
[tex]\[ P(\text{side effects} \mid \text{child}) = \frac{\text{Number of children with side effects}}{\text{Total number of children}} \][/tex]
From the table, the number of children with side effects is 20, and the total number of children is 50. Therefore:
[tex]\[ P(\text{side effects} \mid \text{child}) = \frac{20}{50} = 0.40 \][/tex]
### Conclusion:
Based on the calculated probabilities:
- [tex]\( P(\text{side effects} \mid \text{adult}) = 0.12 \)[/tex]
- [tex]\( P(\text{side effects} \mid \text{child}) = 0.40 \)[/tex]
We can conclude that children have a significantly higher chance of experiencing side effects from the drug compared to adults.
Thus, option B is correct:
```
B. [tex]\( P(\text{side effects} \mid \text{child}) = 0.40 \)[/tex]
[tex]\( P(\text{side effects} \mid \text{adult}) = 0.12 \)[/tex]
Conclusion: Children have a much higher chance of having side effects than adults.
```
