Question

Оптовая база снабжает 10 магазинов, от каждого из которых может поступить заявка в любой день с вероятностью 0,4. Найти вероятность того, что поступят заявки в один день от 3 магазинов.

Answer 1

Ответ: p≈0,215.

Пошаговое объяснение:

Так как заявки от магазинов поступают независимо, то "испытания", под которыми в данном случае подразумевается работа каждого из 10 магазинов в течение одного дня, проводятся "по схеме Бернулли". Тогда искомая вероятность p=C(10,3)*p³*q¹⁰⁻³, где C(10,3) - число сочетаний из 10 по 3, p=0,4 - вероятность поступления заявки от магазина, q=1-p=0,6 - вероятность непоступления заявки. Отсюда p=C(10,3)*(0,4)³*(0,6)⁷≈0,215.

Answer 2

Probability of Receiving Requests from 3 Stores

To find the probability that requests will be received from exactly 3 stores in one day, we can use the binomial distribution formula. The binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent Bernoulli trials.

In this case, we have 10 stores, and each store has a probability of 0.4 of submitting a request on any given day. We want to find the probability of receiving requests from exactly 3 stores.

The binomial distribution formula is as follows:

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

Where: - P(X = k) is the probability of getting exactly k successes - n is the total number of trials (number of stores in this case) - k is the number of successes (number of stores from which requests are received in this case) - p is the probability of success in a single trial (probability of a store submitting a request in this case) - C(n, k) is the number of combinations of n items taken k at a time (n choose k)

Using this formula, we can calculate the probability as follows:

P(X = 3) = C(10, 3) * 0.4^3 * (1 - 0.4)^(10 - 3)

Now let's calculate this probability.

Calculation

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

P(X = 3) = C(10, 3) * 0.4^3 * (1 - 0.4)^(10 - 3)

Where: - C(10, 3) is the number of combinations of 10 items taken 3 at a time, which can be calculated as 10! / (3! * (10 - 3)!) = 120 - 0.4^3 is the probability of getting 3 successes (requests) from a single store, which is 0.064 - (1 - 0.4)^(10 - 3) is the probability of getting 7 failures (no requests) from the remaining stores, which is 0.028

Plugging in these values, we get:

P(X = 3) = 120 * 0.064 * 0.028 ≈ 0.215

Therefore, the probability of receiving requests from exactly 3 stores in one day is approximately 0.215.

Note: The search results provided by You.com did not contain relevant information for this specific question. Therefore, the calculation was done using the binomial distribution formula.