Question

Suppose a population contains 100,000 individuals, of which 500 are carriers of a certain genetic defect. Which of the following is an appropriate way to express this result in terms of odds?

1) The odds of carrying the genetic defect are 5 to 995.
2) The odds of carrying the genetic defect are 500 out of 100,000.
3) The odds of carrying the genetic defect are 500 to 1.

Answer 1

The correct odds of being a carrier of the genetic defect in a population of 100,000 with 500 carriers is 1 to 199. This is obtained by taking the ratio of carriers to non-carriers.

Step-by-step explanation:

The appropriate way to express the odds of an individual in the population being a carrier of a genetic defect when there are 500 carriers in a population of 100,000 individuals is "1 to 199" (option 1, but with correct numbers). This is because odds are typically expressed as the ratio of the number of events that can happen to the number that cannot. In this case, there are 500 possible carriers and 99,500 individuals who are not carriers. Expressing this as option 2, "500 out of 100,000," would describe the probability rather than the odds.

Option 3, "500 to 1," would inaccurately represent the odds as it suggests that for every non-carrier there are 500 carriers, which is not the case here. Therefore, the corrected odds are represented by taking the number of carriers and non-carriers into account: 500 to 99,500, which simplifies to 1 to 199. This means for every one carrier, there are 199 non-carriers.