Question
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?
Answers
GPT 3.5
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%.
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%.