Question

Вероятность того, чтопокупателю потребуется обувь 41-го размера , равна 0,2. Найти вероятность того, что из 5 покупателей обувь этого размера понадобится по крайней мере одному?

Answer 1

Для решения задачи необходимо использовать формулу  вероятности наступления хотя бы одного события.
Задачу можно перефразировать: найти вероятность того. что обувь 41-го размера потребуется одному и более покупателям из пяти возможных.
Найдем вероятность того, что обувь этого размера не потребуется ни одному покупателю.
По формуле Бернулли 

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 at least one customer needing size 41 shoes out of 5 customers

To find the probability that at least one out of five customers will need size 41 shoes, we can use the complement rule.

The complement rule states that the probability of an event not happening is equal to 1 minus the probability of the event happening. In this case, the event is that none of the five customers will need size 41 shoes.

Let's calculate the probability of none of the five customers needing size 41 shoes: - The probability that a customer does not need size 41 shoes is 1 minus the probability that they do need size 41 shoes, which is 1 - 0.2 = 0.8. - Since the customers are independent of each other, we can multiply the probabilities together for each customer. - Therefore, the probability that none of the five customers will need size 41 shoes is 0.8^5 = 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: - Probability of at least one customer needing size 41 shoes = 1 - 0.32768 = 0.67232.

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