Question

Вероятность того, что покупателю потребуется обувь 410го размера равна 0,2. Найти вероятность того, что из 5 первых покупателей обувь этого размера понадобится: а) одному покупателю б) по крайней мере одному покупателю в) ровном двум покупателям

Answer 1

Ответ:

Пошаговое объяснение:

a)

Одному 41 (вероятность 0.2) остальным НЕ 41 (вероятность (0.8)

Итого: 0,2*0,8*0,8*0,8*0,8 = 0,08192

б)

Хотя бы одному 41, обратное событие когда всем НЕ 41...

Если всем не 41 - то 0,8^5 = 0,32768

Значит искомая вероятность = 1 - 0,32768 = 0,67232

(если что ^ это степень)

Answer 2

Probability of a Customer Needing Size 41 Shoes

The probability that a customer will need size 41 shoes is given as 0.2

Probability of One Customer Needing Size 41 Shoes

To find the probability that out of the first 5 customers, one customer will need size 41 shoes, we can use the binomial probability formula. The formula is:

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

Where: - P(X = k) is the probability of exactly k successes - C(n, k) is the number of combinations of n items taken k at a time - p is the probability of success on a single trial - n is the number of trials

In this case, we want to find the probability of one customer needing size 41 shoes, so k = 1, p = 0.2, and n = 5. Plugging these values into the formula, we get:

P(X = 1) = C(5, 1) * 0.2^1 * (1-0.2)^(5-1)

Calculating this, we find:

P(X = 1) = 5 * 0.2 * 0.8^4 ≈ 0.4096

Therefore, the probability that one customer out of the first 5 customers will need size 41 shoes is approximately 0.4096.

Probability of At Least One Customer Needing Size 41 Shoes

To find the probability that at least one customer out of the first 5 customers will need size 41 shoes, we can use the complement rule. The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.

In this case, the event is that none of the first 5 customers need size 41 shoes. The probability of this event can be calculated using the binomial probability formula as follows:

P(X = 0) = C(5, 0) * 0.2^0 * (1-0.2)^(5-0)

Calculating this, we find:

P(X = 0) = 1 * 1 * 0.8^5 = 0.32768

Therefore, the probability that none of the first 5 customers will need size 41 shoes is 0.32768.

Now, we can find the probability of at least one customer needing size 41 shoes by subtracting the probability of none of the customers needing size 41 shoes from 1:

P(at least one customer needs size 41 shoes) = 1 - P(X = 0) = 1 - 0.32768 ≈ 0.67232

Therefore, the probability that at least one customer out of the first 5 customers will need size 41 shoes is approximately 0.67232.

Probability of Exactly Two Customers Needing Size 41 Shoes

To find the probability that exactly two customers out of the first 5 customers will need size 41 shoes, we can again use the binomial probability formula.

Using the formula, with k = 2, p = 0.2, and n = 5, we get:

P(X = 2) = C(5, 2) * 0.2^2 * (1-0.2)^(5-2)

Calculating this, we find:

P(X = 2) = 10 * 0.2^2 * 0.8^3 ≈ 0.2048

Therefore, the probability that exactly two customers out of the first 5 customers will need size 41 shoes is approximately 0.2048.