Question

creating a two-way table from a scenario

in a study, 1,085 out of 2,321 people did not receive a flu vaccination. 465 people were vaccinated and tested positive for the flu. a total of 1,371 participants tested negative. create a two-way table for this scenario.

use the two-way table to determine the probability of randomly selecting a person who tested positive for the flu, given he or she was vaccinated.

\\(\bigcirc\\) \\(\frac{465}{2,321}\\)

\\(\bigcirc\\) \\(\frac{465}{1,236}\\)

\\(\bigcirc\\) \\(\frac{465}{950}\\)

\\(\bigcirc\\) \\(\frac{465}{485}\\)

Explanation:

Identify the given values from the table

Using the Two-Way Frequency Tables knowledge point

$$
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$$

Apply the conditional probability formula

Using the Conditional Probability Calculation knowledge point

$$ P(\text{Positive} \mid \text{Vaccinated}) = \frac{n(\text{Positive} \cap \text{Vaccinated})}{n(\text{Vaccinated})} = \frac{465}{1,236} $$

Answer:

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