Question
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.
What is the probability that exactly 21 of them used Google
What is the probability that exactly 21 of them used Google
Answers
GPT 3.5
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%.
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%.