To solve this problem, we'll compare the probabilities of adults and children experiencing side effects from the drug testing. Here's a step-by-step solution:
1. Gather the Given Data:
- Number of adults with side effects: 6
- Total number of adults: 50
- Number of children with side effects: 20
- Total number of children: 50
2. Calculate the Probability of Side Effects for Adults:
The probability that an adult has side effects (P(side effects|adult)) can be determined by dividing the number of adults with side effects by the total number of adults.
[tex]\[
P(\text{side effects}|\text{adult}) = \frac{\text{Number of adults with side effects}}{\text{Total number of adults}} = \frac{6}{50} = 0.12
\][/tex]
3. Calculate the Probability of Side Effects for Children:
Similarly, the probability that a child has side effects (P(side effects|child)) is determined by dividing the number of children with side effects by the total number of children.
[tex]\[
P(\text{side effects}|\text{child}) = \frac{\text{Number of children with side effects}}{\text{Total number of children}} = \frac{20}{50} = 0.40
\][/tex]
4. Compare the Probabilities:
Now that we have both probabilities:
- P(side effects|adult) = 0.12
- P(side effects|child) = 0.40
Comparing these values, we can see that the probability of a child experiencing side effects is significantly higher than that of an adult. Specifically, the probability for children (0.40) is more than three times higher than that for adults (0.12).
5. Draw a Conclusion Based on the Comparisons:
Given our calculations:
- Since P(side effects|child) = 0.40 and P(side effects|adult) = 0.12, we can conclude that children have a much greater chance of having side effects than adults.
This matches with option C:
- [tex]\( P(\text{side effects}| \text{child}) = 0.40 \)[/tex]
- [tex]\( P(\text{side effects}| \text{adult}) = 0.12 \)[/tex]
- Conclusion: "Children have a much greater chance of having side effects than adults."
So, the correct choice is option C.
