Q:

# If there is three people picked at random from a sample group of 285, 90 of which did not respond, what is the probability that at least one did not respond to this question?

Accepted Solution

A:
To find the probability that at least one person did not respond to the question when three people are picked at random from a sample group of 285, where 90 did not respond, we can use the concept of complementary probability. Let's calculate the probability that all three people responded, and then subtract that probability from 1 to get the probability that at least one did not respond. Probability that a randomly picked person responded = (Total responders) / (Total sample size) P(responder) = (285 - 90) / 285 = 195 / 285 Probability that all three picked people responded = P(responder) * P(responder) * P(responder) P(all responded) = (195 / 285) * (195 / 285) * (195 / 285) Now, the probability that at least one did not respond = 1 - P(all responded) P(at least one did not respond) = 1 - P(all responded) Let's calculate this: P(at least one did not respond) = 1 - ((195 / 285) * (195 / 285) * (195 / 285)) This will give you the probability that at least one person did not respond when three people are picked at random from the sample group.