Question

the data
$a_{11}=7$, $a_{12}=4$, $a_{13}=20$, $a_{21}=196$, $a_{22}=175$, $a_{23}=161$
which is represented in the following table, were derived from a study of the effectiveness of
a flu vaccine. the value in each cell of the table represents the number of individuals in that
category. some participants in the study were given no vaccine, some were given one
injection, and some were given two injections.

what is the probability that a person received one injection and got the flu?
note: for any final answer that has up to four decimal places, enter your answer without rounding
the number. for any answers with more than four decimal values, round your final answer to four
decimal places.

Explanation:

Step1: Calculate total number of participants

Add up all the values in the table: \(7 + 4+20 + 196+175 + 161\)

$$
LATEXBLOCK0
$$

Step2: Find the number of people who received one injection and got the flu

From the table, this value is \(a_{12}=4\)

Step3: Calculate the probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\), so \(P=\frac{4}{563}\approx0.0071\)

Answer:

\(0.0071\)