On average, every one out of 10 telephones is found busy. Six telephone numbers are selected at random. Find the probability that four of them will be busy.
Question
On average, every one out of 10 telephones is found busy. Six telephone numbers are selected at random. Find the probability that four of them will be busy.
Solution
To find the probability that four out of six telephone numbers will be busy, we can use the concept of binomial probability.
The probability of a telephone being busy is 1 out of 10, or 1/10. Therefore, the probability of a telephone not being busy is 9 out of 10, or 9/10.
To calculate the probability of four out of six telephones being busy, we can use the binomial probability formula:
P(X=k) = (nCk) * p^k * (1-p)^(n-k)
Where: P(X=k) is the probability of getting exactly k successes (in this case, k busy telephones) n is the total number of trials (in this case, 6 telephone numbers selected) k is the number of successful outcomes (in this case, 4 busy telephones) p is the probability of success (in this case, 1/10)
Using this formula, we can calculate the probability as follows:
P(X=4) = (6C4) * (1/10)^4 * (9/10)^(6-4)
Calculating the values:
(6C4) = 6! / (4! * (6-4)!) = 6! / (4! * 2!) = (6 * 5) / (2 * 1) = 15
(1/10)^4 = 1/10 * 1/10 * 1/10 * 1/10 = 1/10,000
(9/10)^(6-4) = (9/10)^2 = 81/100
Now, we can substitute these values into the formula:
P(X=4) = 15 * (1/10,000) * (81/100) = 0.01215
Therefore, the probability that four out of six telephone numbers will be busy is approximately 0.01215, or 1.215%.
Similar Questions
The number of phone calls per five minutes in an office has a mean of six.(a) What is the probability there will be exactly five calls in a five-minute period?[1](b) What is the probability there will be exactly four calls in a four-minute period?[2](c) What is the probability there will be more than two calls in a five-minute period?[2](d) What is the probability there will be fewer than five calls in a five-minute period?
A Customer Telephone Center receives 1,200 calls in a 24-hour period. Of these calls, 75% occur between 9:30 a.m. and 3:30 p.m., and calls are evenly distributed during this time. If each person handles 10 calls an hour, how many people are needed to handle calls during these hours?2018515
The number of times a hotline receives calls per minute obeys a Poisson distribution with a parameter of 4. Find the probability that exactly 8 calls are received in a certain minute.(The result is accurate to 4 decimal places)
There are 10 stations at your new job. Your manager trains you on 4 stations at random. What is the probability that you are not trained on the most desirable station? Probability: %
A nine-digit mobile number consists of exactly four zeroes. One of the digits is repeated twice. The remaining three digits are all distinct. If the first four digits (from left to right) are 8098, then find the probability of having only one 9, one 1, and one 2 in the mobile number. Ops: A. 2/17 B. 1/21 C. 1/15 D. 4/13
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.