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? Round answer to four decimal places

Answer 1

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

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

where:
n = 25 (total number of searches)
k = 20 (number of searches using Google)
p = 0.67 (probability of using Google)

Plugging in the values:

P(X = 20) = (25 choose 20) * (0.67)^20 * (0.33)^5

Calculating the values:

P(X = 20) = (25! / (20! * 5!)) * (0.67)^20 * (0.33)^5
P(X = 20) = 53,130 * 0.00000447 * 0.002275

P(X = 20) = 0.2455

Therefore, the probability that exactly 20 out of 25 searches use Google is 0.2455 (rounded to four decimal places).