A survey found that 10% of people believe that they have seen a UFO. Choose a sample of 13 people at random. Find the probability that 1) At least 3 people believe that they have seen a UFO

Question

A survey found that 10% of people believe that they have seen a UFO. Choose a sample of 13 people at random. Find the probability that

1) At least 3 people believe that they have seen a UFO

2.) 5 or 6 people believe that they have seen a UFO

3) Exactly 2 people believe that they have seen a UFO

Answer 1

This fits the requirements for using the binomial probability formula:

P(x successes in n tries) = n!/([x!(n-x)!) * p^x * (1-p) ^ (n-x)

where p is the probability of success (0.1) and n = sample size = 13

For example P(x = 5) = 13!/(5!8!) * 0.1^5 * 0.9*8

for 1) P(x >= 3) = 1 - P(x <= 2) = 1 - [ P(x = 0) + P(x = 1) + P(x = 2)]

2) P(x = 5 or x = 6) = P(x = 5) + P(x = 6)

3) P(x = 2)