Question

вероятность того, что любой абонент позвонит на коммутатор в течение часа равна 0,01. телефонная станция обслуживает 780 абонентов. какова вероятность того, что в течение часа позвонят не менее 4 абонентов?

Answer 1

  распределение Пуассона
n=800 p=0/01 лямбда= np = 800* 0.01=8
P(k)= (лямбда)^k / k! * e^(-лямбда)
P(5)= 8^5/5! * e^(-8) 

Answer 2

Probability of an individual subscriber making a call within an hour

According to the information provided, the probability of any subscriber making a call to the switchboard within an hour is 0.01.

Number of subscribers serviced by the telephone station

The telephone station services 780 subscribers.

Probability of at least 4 subscribers making a call within an hour

To calculate the probability of at least 4 subscribers making a call within an hour, we can use the concept of the binomial distribution. The binomial distribution is used to calculate the probability of a certain number of successes (in this case, subscribers making a call) in a fixed number of trials (in this case, the number of subscribers).

The formula for the probability of at least k successes in n trials is:

P(X >= k) = 1 - P(X < k)

Where P(X >= k) is the probability of at least k successes, P(X < k) is the probability of less than k successes, and X is a random variable representing the number of successes.

In this case, we want to calculate the probability of at least 4 subscribers making a call within an hour. Let's denote this as P(X >= 4).

Using the binomial distribution formula, we can calculate the probability as follows:

P(X >= 4) = 1 - P(X < 4)

To calculate P(X < 4), we need to calculate the probabilities of 0, 1, 2, and 3 subscribers making a call and sum them up.

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

To calculate these probabilities, we can use the binomial probability formula:

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

Where C(n, k) is the number of combinations of n items taken k at a time, p is the probability of success (in this case, the probability of a subscriber making a call), and n is the number of trials (in this case, the number of subscribers).

Let's calculate the probabilities:

P(X = 0) = C(780, 0) * 0.01^0 * (1 - 0.01)^(780 - 0) P(X = 1) = C(780, 1) * 0.01^1 * (1 - 0.01)^(780 - 1) P(X = 2) = C(780, 2) * 0.01^2 * (1 - 0.01)^(780 - 2) P(X = 3) = C(780, 3) * 0.01^3 * (1 - 0.01)^(780 - 3)

We can then calculate P(X < 4) by summing up these probabilities.

Finally, we can calculate P(X >= 4) by subtracting P(X < 4) from 1.

Please note that the calculations involved in this process are quite extensive and may require a calculator or software to perform accurately.