Question

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? 

Answer 1

49 %

465 + 485 = 950

465/950 = .489

.489 * 100 = 48.9, round up for 49 to get 49%, since it's only focused on people who tested positive, you would only have to compare the people in that column

Answer 2

Answer:

The probability that a randomly selected person who is tested positive is vaccinated is:

0.4895

Step-by-step explanation:

We are given a two-way frequency table that represents the result of a recent study on the effectiveness of the flu vaccine.

The table is as follows:

                                  Pos.              Neg.                Total

Vaccinated                465                771                   1236

Not vaccinated         485                 600                 1085  

Total                           950               1371                   2321

Now we are asked to find the probability that a randomly selected person who tested positive for the flu is vaccinated.

Let A denote the event that the person is tested positive.

Let B denote the vent that he/she is vaccinated.

A∩B denote the event that the person tested positive is vaccinated.

Let P denote the probability of an event.

We are asked to find:

P(B|A)

We know that:

$P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}$

From the table we have:

$P(A\bigcap B)=\dfrac{465}{2321}$

and

$P(A)=\dfrac{950}{2321}$

Hence,

$P(B|A)=\dfrac{\dfrac{465}{2321}}{\dfrac{950}{2321}}\\\\P(B|A)=\dfrac{465}{950}\\\\P(B|A)=0.4895$

Hence, the probability is:

0.4895