Let's analyze the problem step-by-step to find the probabilities and draw the correct conclusion.
1. Determine the probability that an adult has side effects:
- The total number of adults is 50.
- The number of adults who experienced side effects is 7.
- The probability [tex]\( P(\text{side effects} \mid \text{adult}) \)[/tex] is calculated as:
[tex]\[
P(\text{side effects} \mid \text{adult}) = \frac{\text{Number of adults with side effects}}{\text{Total number of adults}} = \frac{7}{50} = 0.14
\][/tex]
2. Determine the probability that a child has side effects:
- The total number of children is 50.
- The number of children who experienced side effects is 22.
- The probability [tex]\( P(\text{side effects} \mid \text{child}) \)[/tex] is calculated as:
[tex]\[
P(\text{side effects} \mid \text{child}) = \frac{\text{Number of children with side effects}}{\text{Total number of children}} = \frac{22}{50} = 0.44
\][/tex]
3. Draw the conclusion based on the probabilities:
- The probability of a child having side effects (0.44) is greater than the probability of an adult having side effects (0.14).
- Therefore, we can conclude that children have a much greater chance of having side effects than adults.
So, the correct answer is A:
[tex]\[
P(\text{side effects} \mid \text{child}) = 0.44, \quad P(\text{side effects} \mid \text{adult}) = 0.14
\][/tex]
Conclusion: Children have a much greater chance of having side effects than adults.
