According to a recent report 66%of Internet searches in a month used Google search engine. Assume that a sample of 24 searches are studied. Round answers to four decimal places.

Question

What is the probability that exactly 21 of them used Google

Answer 1

To calculate the probability that exactly 21 out of 24 searches used Google, we can use the binomial probability formula:

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

where:
P(X = k) is the probability that exactly k successes occur
n is the total number of trials (sample size) = 24
k is the number of successful outcomes = 21
p is the probability of success on an individual trial = 0.66
(1-p) is the probability of failure on an individual trial = 0.34

Plugging in the values:

P(X = 21) = (24 choose 21) * (0.66)^21 * (0.34)^3

Calculating (24 choose 21):

(24 choose 21) = 24! / (21! * (24-21)!) = 24! / (21! * 3!) = 2024

Now, plug in to the formula:

P(X = 21) = 2024 * (0.66)^21 * (0.34)^3
P(X = 21) = 2024 * 0.0089807 * 0.0393034
P(X = 21) = 0.7081

Therefore, the probability that exactly 21 out of 24 searches used Google is approximately 0.7081 or 70.81%.