According to a recent report, 67% of Internet searches in a particular month used the Google search engine. Assume that a sample of 25 searches is studied. What's the probability that exactly 20 of them used Google?

Answer 1

To find the probability that exactly 20 of the 25 searches used Google, we can use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where:
- n is the total number of trials (25 searches)
- k is the number of successful outcomes (20 searches using Google)
- p is the probability of success on a single trial (67% or 0.67)

Plugging in the values:

P(X = 20) = (25 choose 20) * 0.67^20 * (1-0.67)^(25-20)

= (25! / (20! * (25-20)!)) * 0.67^20 * 0.33^5

= 53,130 * 0.067 * 0.002977

= 9.48

Therefore, the probability that exactly 20 of the 25 searches used Google is 9.48%.