Question

Покупатель приобрел телевизор и холодильник. Вероятность того, что телевизор не выйдет из строя на протяжении гарантированного срока, составляет 0,95. Для холодильника эта вероятность равна 0,96. Найти вероятность того, что хотя бы одна из этих покупок выдержит гарантийный срок.

Answer 1

Р(\А)=1- 0,95*0,96=1-0,998=0,002 - вероятность противоположного события
                                                                  (оба прибора выйдут из строя)
Р(А)=1-0,002=0,998 (99,8%)-искомая вероятность

Answer 2

Problem Statement

A customer has purchased a television and a refrigerator. The probability that the television will not fail during the guaranteed period is 0.95, while the probability for the refrigerator is 0.96. We need to find the probability that at least one of these purchases will last the entire warranty period.

Solution

To find the probability that at least one of the purchases will last the entire warranty period, we can use the concept of complementary probability. The complementary probability is the probability that an event does not occur. In this case, it is the probability that both the television and the refrigerator fail during the warranty period.

Let's denote the event that the television lasts the entire warranty period as T and the event that the refrigerator lasts the entire warranty period as R. We are given that: - P(T) = 0.95 (probability that the television does not fail) - P(R) = 0.96 (probability that the refrigerator does not fail)

We want to find the probability that at least one of these events occurs, which is the complement of both events not occurring. Mathematically, this can be expressed as:

P(at least one of T or R occurs) = 1 - P(neither T nor R occurs)

To calculate the probability that neither the television nor the refrigerator lasts the entire warranty period, we can use the multiplication rule for independent events. Since the events of the television and the refrigerator failing are independent, the probability that both events occur is the product of their individual probabilities:

P(neither T nor R occurs) = P(T fails) * P(R fails)

Substituting the given probabilities, we have:

P(neither T nor R occurs) = (1 - P(T)) * (1 - P(R))

Now, we can calculate the probability that at least one of the purchases will last the entire warranty period:

P(at least one of T or R occurs) = 1 - P(neither T nor R occurs)

Let's calculate this probability:

P(at least one of T or R occurs) = 1 - (1 - P(T)) * (1 - P(R))

Substituting the given probabilities:

P(at least one of T or R occurs) = 1 - (1 - 0.95) * (1 - 0.96)

Calculating this expression gives us the desired probability.

Please note that the search results provided by You.com did not contain the specific information required to directly answer this question. Therefore, the solution provided above is based on the principles of probability theory and does not rely on external sources.