Question

5. В магазине стоят два платёжных автомата. Каждый из них может быть неисправен с вероятностью 0,2 независимо от другого автомата. Найдите вероятность того, что хотя бы один автомат исправен помогите пожайлуста решить задание

Answer 1

В этой задаче также предполагается независимость работы автоматов.
Найдем вероятность противоположного события
 = {оба автомата неисправны}.
Для этого используем формулу умножения вероятностей независимых событий:
Р(А)= 0,2*0,2=0,04
Значит, вероятность события  = {хотя бы один автомат исправен} равна 
Р(А)= 1-Р(А) = 1- 0,04=0,96

Answer 2

Problem Analysis

We are given two payment machines in a store, and each machine can be faulty with a probability of 0.2 independently of the other machine. We need to find the probability that at least one machine is working.

Solution

To find the probability that at least one machine is working, we can use the complement rule. The complement of the event "at least one machine is working" is the event "both machines are faulty." Therefore, we can find the probability of the complement and subtract it from 1 to get the desired probability.

Let's calculate the probability of both machines being faulty first. Since the probability of each machine being faulty is 0.2, the probability of both machines being faulty is the product of their individual probabilities: 0.2 * 0.2 = 0.04.

Now, we can find the probability of at least one machine being working by subtracting the probability of both machines being faulty from 1: 1 - 0.04 = 0.96.

Therefore, the probability that at least one machine is working is 0.96.

Answer

The probability that at least one machine is working is 0.96.