To compare the probabilities of side effects between adults and children, let's break down the steps thoroughly:
1. Identify the relevant data:
- Number of adults with side effects: 7
- Number of adults without side effects: 43
- Number of children with side effects: 22
- Number of children without side effects: 28
- Total number of adults: 50 (7 + 43)
- Total number of children: 50 (22 + 28)
2. Calculate the probability of side effects for adults:
[tex]\[
P(\text{side effects} \mid \text{adult}) = \frac{\text{Number of adults with side effects}}{\text{Total number of adults}}
\][/tex]
Substituting the values, we get:
[tex]\[
P(\text{side effects} \mid \text{adult}) = \frac{7}{50} = 0.14
\][/tex]
3. Calculate the probability of side effects for children:
[tex]\[
P(\text{side effects} \mid \text{child}) = \frac{\text{Number of children with side effects}}{\text{Total number of children}}
\][/tex]
Substituting the values, we get:
[tex]\[
P(\text{side effects} \mid \text{child}) = \frac{22}{50} = 0.44
\][/tex]
4. Comparison and conclusion:
- Probability of side effects for adults: [tex]\(0.14\)[/tex]
- Probability of side effects for children: [tex]\(0.44\)[/tex]
Since [tex]\(0.44\)[/tex] (probability for children) is greater than [tex]\(0.14\)[/tex] (probability for adults), we conclude that children have a greater chance of having side effects compared to adults.
Therefore, the correct option is:
B.
[tex]\[ P(\text{side effects} \mid \text{child}) = 0.44 \][/tex]
[tex]\[ P(\text{side effects} \mid \text{adult}) = 0.14 \][/tex]
Conclusion: Children have a much greater chance of having side effects than adults.
