Question

question 5 of 10 a medical company tested a new drug on 100 people for possible side effects. this table shows the results. 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. ( p(\text{side effects|child}) = 0.40 ) ( p(\text{side effects|adult}) = 0.12 ) conclusion: children have a much lower chance of having side effects than adults. b. ( p(\text{side effects|child}) = 0.20 ) ( p(\text{side effects|adult}) = 0.60 ) conclusion: children have a much greater chance of having side effects than adults

Explanation:

Step1: Calculate \(P(\text{side effects|child})\)

The formula for conditional probability \(P(A|B)=\frac{n(A\cap B)}{n(B)}\). Here, for children, \(n(\text{side effects}\cap\text{child}) = 20\) and \(n(\text{child})=50\). So \(P(\text{side effects|child})=\frac{20}{50}=0.40\)

Step2: Calculate \(P(\text{side effects|adult})\)

For adults, \(n(\text{side effects}\cap\text{adult}) = 6\) and \(n(\text{adult}) = 50\). So \(P(\text{side effects|adult})=\frac{6}{50}=0.12\)
Since \(0.40>0.12\), the conclusion “Children have a much lower chance of having side effects than adults” in option A is wrong. But based on the calculation of conditional - probability values in option A (\(P(\text{side effects|child}) = 0.40\), \(P(\text{side effects|adult}) = 0.12\)) which are correct according to the formula \(P(A|B)=\frac{n(A\cap B)}{n(B)}\), while in option B the probability values are calculated wrong (\(\frac{20}{50}
eq0.20\) and \(\frac{6}{50}
eq0.60\))

Answer:

A. \( P(\text{side effects|child}) = 0.40\), \(P(\text{side effects|adult}) = 0.12\)