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A medical company tested a new drug on 100 people for possible side effects. This table shows the results.

\begin{tabular}{|l|c|c|c|}
\hline
& Side effects & No side effects & Total \\
\hline
Adults & 6 & 44 & 50 \\
\hline
Children & 20 & 30 & 50 \\
\hline
Total & 26 & 74 & 100 \\
\hline
\end{tabular}

Compare the probability that an adult has side effects with the probability that a child has side effects. Draw a conclusion based on your results.

A. [tex]$P$[/tex](side effects [tex]$\mid$[/tex] child) = 0.40, [tex]$P$[/tex](side effects [tex]$\mid$[/tex] adult) = 0.12
Conclusion: Children have a higher chance of having side effects than adults.

B. [tex]$P$[/tex](side effects [tex]$\mid$[/tex] child) = 0.20

Sagot :

GinnyAnswer
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.
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