If the risk of getting influenza virus among fully vaccinated people was 0.25, how much is the odd for getting influenza among the fully vaccinated people?
Understand the Problem
The question is asking us to calculate the odds of getting influenza among fully vaccinated people, given that the risk (probability) of getting influenza is 0.25. The odds are calculated as the probability of the event occurring divided by the probability of the event not occurring. In this case, that would be P(influenza) / (1 - P(influenza)).
Answer
0. 33
Answer for screen readers
B. 0.33
Steps to Solve
- Calculate the probability of not getting influenza
We are given that the probability of getting influenza is 0.25. The probability of not getting influenza is $1 - 0.25$.
$1 - 0.25 = 0.75$
- Calculate the odds of getting influenza
The odds of getting influenza are calculated as the probability of getting influenza divided by the probability of not getting influenza:
$Odds = \frac{P(influenza)}{P(no\ influenza)} = \frac{0.25}{0.75}$
- Simplify the fraction
Simplify the fraction $\frac{0.25}{0.75}$
$\frac{0.25}{0.75} = \frac{1}{3} \approx 0.33$
B. 0.33
More Information
The odds represent the ratio of the probability of an event occurring to the probability of it not occurring. In this case, for every 1 person who gets the flu, there are approximately 3 people who do not.
Tips
A common mistake is to confuse probability with odds. Probability is the likelihood of an event occurring, while odds are the ratio of the probability of an event occurring to the probability of it not occurring. Another mistake would be to not do the subtraction correctly or divide in the wrong order.
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