Question

About 33% of people who get their feet examined are found to have an ingrown toenail. What is the probability of a podiatrist examining seven people until he finds the first patient who has an ingrown toenail?

(0.33)6
(0.67)6
(0.33)6(0.67)1
(0.67)6(0.33)1
1 − (0.33)6

Answer 1

The probability of a podiatrist finding the first patient with an ingrown toenail after examining seven people is calculated using the geometric distribution formula. It involves six failures (not having an ingrown toenail) followed by one success (having an ingrown toenail), which is mathematically represented as (0.67)^6 * (0.33).

Step-by-step explanation:

The question is asking about the probability of a podiatrist finding the first patient with an ingrown toenail after examining seven people, given that there is about a 33% chance of any examined person having an ingrown toenail. This type of problem can be solved using the concept of geometric distribution, which pertains to the number of trials needed for the first success in a series of independent and identically distributed Bernoulli trials.

To find the probability of the podiatrist first encountering an ingrown toenail on the seventh examination, we need the first six to not have an ingrown toenail and the seventh person to have one. The probability of not having an ingrown toenail is 1 - 0.33, which is 0.67. So, the probability we're looking for is (0.67)6 multiplied by (0.33), which represents six failures followed by one success.