If prevalence of diabetes is 10%, the probability that three people selected at random from the population will have diabetes is –
## Core Concept
The problem involves calculating the probability of a specific event (three people having diabetes) occurring in a population with a given prevalence of diabetes (10%). This is a classic example of a binomial probability problem in statistics.
## Why the Correct Answer is Right
To calculate the probability that three people selected at random from the population will have diabetes, we use the binomial probability formula. However, given that we are looking for the probability of all three having diabetes, we can simply multiply the probability of one person having diabetes by itself three times (since the selection of each person is independent). The probability of one person having diabetes is 10% or 0.1. So, the probability that all three will have diabetes is (0.1 times 0.1 times 0.1 = 0.1^3 = 0.001) or 0.1%.
## Why Each Wrong Option is Incorrect
- **Option A:** This option suggests a calculation that doesn't match the scenario described. Without calculating, we know it's incorrect because it doesn't align with the simple multiplication of probabilities for independent events.
- **Option B:** Similarly, this option does not align with the correct calculation of (0.1^3).
- **Option D:** This option suggests a much higher probability than what would be expected from multiplying 0.1 by itself three times.
## Clinical Pearl / High-Yield Fact
Remember, when dealing with probabilities of disease in populations, understanding the basics of statistics, such as the multiplication rule for independent events, is crucial. In this case, a 10% prevalence means that for every 10 people, 1 has diabetes. Thus, the chance of three in a row having diabetes is indeed very low, specifically 0.1% or 1 in 1000.
## Correct Answer Line
**Correct Answer: C. 0.1%**