Question

calculating a conditional probability

the two-way table shows the results of a recent study on the effectiveness of the flu vaccine.

what is the probability that a randomly selected person who tested positive for the flu is vaccinated?

\\(\bigcirc\\) \\(\frac{465}{2,321}\\)
\\(\bigcirc\\) \\(\frac{465}{1,236}\\)
\\(\bigcirc\\) \\(\frac{465}{950}\\)
\\(\bigcirc\\) \\(\frac{465}{485}\\)

Explanation:

Identify the given information and target probability

Using the Two-Way Frequency Tables knowledge point

• The table categorizes individuals by vaccination status (Vaccinated, Not Vaccinated) and flu test results (Pos., Neg.).
• Target: Find the probability that a randomly selected person is vaccinated, given that they tested positive for the flu.

Apply the conditional probability formula

Using the Conditional Probability Calculation knowledge point

$$ P(\text{Vaccinated} \mid \text{Positive}) = \frac{n(\text{Vaccinated} \cap \text{Positive})}{n(\text{Positive})} $$

Extract values and calculate the ratio

Using the Two-Way Frequency Tables and Conditional Probability Calculation knowledge points

$$
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$$

Answer:

• (A) \(\frac{465}{2,321}\)
• (B) \(\frac{465}{1,236}\)
• (C) \(\frac{465}{950}\) (Correct answer)
• (D) \(\frac{465}{485}\)