To solve this problem, we'll determine the probability that adults and children have side effects from the new drug and then compare these probabilities.
1. Calculate the probability that an adult has side effects:
From the table:
- The number of adults with side effects is 6.
- The total number of adults is 50.
The probability [tex]\( P \)[/tex] that an adult has side effects is calculated as follows:
[tex]\[
P(\text{side effects} \mid \text{adult}) = \frac{\text{Number of adults with side effects}}{\text{Total number of adults}} = \frac{6}{50} = 0.12
\][/tex]
2. Calculate the probability that a child has side effects:
From the table:
- The number of children with side effects is 20.
- The total number of children is 50.
The probability [tex]\( P \)[/tex] that a child has side effects is calculated as follows:
[tex]\[
P(\text{side effects} \mid \text{child}) = \frac{\text{Number of children with side effects}}{\text{Total number of children}} = \frac{20}{50} = 0.40
\][/tex]
3. Comparison and Conclusion:
We have the following probabilities:
- [tex]\( P(\text{side effects} \mid \text{adult}) = 0.12 \)[/tex]
- [tex]\( P(\text{side effects} \mid \text{child}) = 0.40 \)[/tex]
Comparing these probabilities, we can see that [tex]\( P(\text{side effects} \mid \text{child}) \)[/tex] is greater than [tex]\( P(\text{side effects} \mid \text{adult}) \)[/tex].
Therefore, the conclusion is that children have a higher chance of having side effects than adults.
Given these steps and the results, the correct answer is:
C. [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 higher chance of having side effects than adults.
