To compare the probability that an adult experiences side effects with the probability that a child experiences side effects, let's analyze the given data step-by-step.
### Step-by-Step Solution:
1. Extract Given Data:
- Total number of adults: 50
- Number of adults with side effects: 7
- Total number of children: 50
- Number of children with side effects: 22
2. Calculate the Probability for Adults:
- The probability that an adult has side effects (P(side effects | adult)) can be calculated by dividing the number of adults with side effects by the total number of adults.
- [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]
3. Calculate the Probability for Children:
- The probability that a child has side effects (P(side effects | child)) can be calculated by dividing the number of children with side effects by the total number of children.
- [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]
4. Compare the Probabilities:
- The probability that an adult has side effects is [tex]\(0.14\)[/tex].
- The probability that a child has side effects is [tex]\(0.44\)[/tex].
5. Draw Conclusion:
- From the calculated probabilities, [tex]\(0.14\)[/tex] for adults and [tex]\(0.44\)[/tex] for children, we observe that the probability for children is significantly higher.
- We conclude that:
[tex]\[
\text{Children have a much greater chance of having side effects than adults.}
\][/tex]
### Final Answer:
Based on the calculations and the comparison, the answer is option 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.
