Question

Техническое устройство состоит из 4 блоков, вероятности выхода из работы каждого из которых равны 0,1. Для работы устройства необходимо отлажена работа всех 4-х блоков. Найти вероятность настроенной работы устройства​

Answer 1

Ответ:

Пошаговое объяснение:

Вероятность выхода элемента из работы:

q = 0,1.

Вероятность того, что блок рабочий:

p = 1 - q = 1 - 0,1 = 0,9

Пусть:

A - событие, заключающееся в том, что устройство настроено.

Вероятность настроенной работы по правилу умножения вероятностей:

P(A) = p·p·p·p = p⁴

P(A) = 0,9⁴ = 0,6561

Answer 2

Technical Device with 4 Blocks

A technical device consists of 4 blocks, each with a probability of failure of 0.1. The device requires all 4 blocks to be functioning properly in order to work. We need to find the probability of the device working correctly.

To find the probability of the device working, we can use the concept of complementary probability. The complementary probability is the probability of the event not occurring. In this case, the event is the device not working.

The probability of the device not working is the probability that at least one of the blocks fails. Since the blocks are independent, we can calculate the probability of each block failing and then subtract it from 1 to get the probability of the device working.

The probability of a block failing is given as 0.1. Therefore, the probability of a block working is 1 - 0.1 = 0.9.

To find the probability of all 4 blocks working, we multiply the probabilities of each block working together:

Probability of all 4 blocks working = (0.9) * (0.9) * (0.9) * (0.9) = 0.6561

Therefore, the probability of the device working correctly is 0.6561 or 65.61%.