Question

в магазине стоят два платежных автомата. Первый автомат может быть неисправен с вероятностью 0,23, а второй с вероятность 0,38. найдите вероятность того, что хотя бы один автомат неисправен

Answer 1

Ответ:

0,9126

Объяснение:

Вероятность того, что оба платёжных автоматов исправны:

0,23·0,38=0,0874

Вероятность того, что хотя бы один автомат исправен:

1-0,0874=0,9126

Answer 2

Problem Analysis

We are given two payment machines in a store. The first machine can be faulty with a probability of 0.23, and the second machine can be faulty with a probability of 0.38. We need to find the probability that at least one of the machines is faulty.

Solution

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

Let's calculate the probability of both machines working fine:

- Probability that the first machine is working fine: 1 - 0.23 = 0.77. - Probability that the second machine is working fine: 1 - 0.38 = 0.62.

To find the probability of both machines working fine, we multiply the probabilities of each machine working fine:

0.77 * 0.62 = 0.4774.

Now, we can subtract this probability from 1 to find the probability that at least one machine is faulty:

1 - 0.4774 = 0.5226.

Therefore, the probability that at least one of the machines is faulty is approximately 0.5226.

Conclusion

The probability that at least one of the two payment machines in the store is faulty is approximately 0.5226.