Question

question 9 (2 points) listen a hospital tracks whether patients receive vaccinations for flu and covid-19. the results are shown below: | | flu vaccination | no flu vaccination | total | | --- | --- | --- | --- | | covid-19 vaccination | 45 | 25 | 70 | | no covid-19 vaccination | 15 | 15 | 30 | | total | 60 | 40 | 100 | what is the probability that a randomly selected patient either received a flu vaccination or a covid-19 vaccination? 0.45 0.75 0.80 0.85 0.90

Explanation:

Step1: Define events and formula

Use the addition rule for probability: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, where $A$ = flu vaccination, $B$ = COVID-19 vaccination.

Step2: Calculate $P(A)$

$P(A) = \frac{\text{Total flu vaccinations}}{\text{Total patients}} = \frac{60}{100} = 0.6$

Step3: Calculate $P(B)$

$P(B) = \frac{\text{Total COVID-19 vaccinations}}{\text{Total patients}} = \frac{70}{100} = 0.7$

Step4: Calculate $P(A \cap B)$

$P(A \cap B) = \frac{\text{Both vaccinations}}{\text{Total patients}} = \frac{45}{100} = 0.45$

Step5: Compute final probability

Substitute values into the addition rule: $P(A \cup B) = 0.6 + 0.7 - 0.45$

Answer:

0.85