Question

question 13
3 pts
the data:
a11 = 5, a12 = 8, a13 = 18, a21 = 273, a22 = 56, a23 = 257
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 two injections?
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 all the values in the table:

$$\begin{align*} \text{Total}&=a_{11}+a_{12}+a_{13}+a_{21}+a_{22}+a_{23}\\ &=5 + 8+18+273+56+257\\ &=(5 + 273)+(8 + 56)+(18+257)\\ &=278+64+275\\ &=617 \end{align*}$$

Step2: Calculate number of participants who received two injections

The number of participants who received two injections is \(a_{13}+a_{23}=18 + 257=275\)

Step3: Calculate the probability

The probability \(P\) that a person received two injections is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)
So \(P=\frac{275}{617}\approx0.4457\)

Answer:

\(0.4457\)