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:

From the table we have:

and

Hence,

Hence, the probability is:
0.4895