Sure! Let's break down the problem step-by-step.
First, we need to determine the probabilities of side effects for each group (adults and children) individually. These are expressed as conditional probabilities.
Given the 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
### Probability for Adults:
The probability that an adult has side effects can be calculated by taking the ratio of the number of adults with side effects to the total number of adults.
[tex]\[ P(\text{side effects} \mid \text{adult}) = \frac{\text{Number of adults with side effects}}{\text{Total number of adults}} \][/tex]
[tex]\[ P(\text{side effects} \mid \text{adult}) = \frac{6}{50} \][/tex]
[tex]\[ P(\text{side effects} \mid \text{adult}) = 0.12 \][/tex]
### Probability for Children:
Similarly, the probability that a child has side effects is the ratio of the number of children with side effects to the total number of children.
[tex]\[ P(\text{side effects} \mid \text{child}) = \frac{\text{Number of children with side effects}}{\text{Total number of children}} \][/tex]
[tex]\[ P(\text{side effects} \mid \text{child}) = \frac{20}{50} \][/tex]
[tex]\[ P(\text{side effects} \mid \text{child}) = 0.4 \][/tex]
### Conclusion:
Comparing these probabilities, we find:
- The probability that an adult has side effects is [tex]\( 0.12 \)[/tex].
- The probability that a child has side effects is [tex]\( 0.4 \)[/tex].
Therefore, option A is the correct interpretation of the data:
- [tex]\( P(\text{side effects} \mid \text{child}) = 0.4 \)[/tex]
- [tex]\( P(\text{side effects} \mid \text{adult}) = 0.12 \)[/tex]
The conclusion is that children have a significantly higher chance of having side effects compared to adults. This contradicts the statement in option A. Hence, the correct interpretation should be:
```
Children have a much higher chance of having side effects than adults.
```
Therefore, the conclusion should be adjusted to reflect this correct comparison.
