Final answer:
To find the probability that at least 3 out of 11 people believe they have seen a UFO, we use the binomial probability formula and subtract the sum of the probabilities of 0, 1, and 2 occurrences from 1.
Step-by-step explanation:
The question asks about the probability that at least 3 out of a sample of 11 people believe they have seen a UFO, given that 20% of people report this belief. To calculate this probability, we use the binomial probability formula:
- P(X = x) = C(n, x) * (p^x) * ((1-p)^(n-x))
Where:
- n is the number of trials (in this case, 11 people)
- x is the number of successes (people who have seen a UFO)
- p is the probability of success on an individual trial (0.20 or 20%)
- C(n, x) is the combination of n items taken x at a time
To find the probability of at least 3 people, we calculate 1 minus the probability of 0, 1, and 2 people having seen a UFO:
Probability of at least 3 = 1 - (P(0) + P(1) + P(2))
After calculating each probability and summing them, we subtract the sum from 1 to get the final probability.