Question

Прилад може належати до однієї з двох партій з ймовірностями 0,45 та 0,55. Надійність приладів цих партій складає відповідно 0,7 та 0,8. Визначте ймовірність того, що придбаний прилад відпрацює гарантійний час

Answer 1

Problem Analysis

We are given that a device can belong to one of two parties, with probabilities of 0.45 and 0.55 respectively. The reliability of the devices from these parties is 0.7 and 0.8 respectively. We need to determine the probability that the purchased device will work for the warranty period.

Solution

To solve this problem, we can use the law of total probability. The probability that the device will work for the warranty period can be calculated by considering the probabilities for each party and their corresponding reliabilities.

Let's denote: - Party A: the party with a probability of 0.45 - Party B: the party with a probability of 0.55 - Reliability of Party A: 0.7 - Reliability of Party B: 0.8

We can calculate the probability of the device working for the warranty period as follows:

Step 1: Calculate the probability of purchasing a device from Party A and it working for the warranty period.

The probability of purchasing a device from Party A is 0.45, and the reliability of devices from Party A is 0.7. Therefore, the probability of a device from Party A working for the warranty period is 0.45 * 0.7 = 0.315.

Step 2: Calculate the probability of purchasing a device from Party B and it working for the warranty period.

The probability of purchasing a device from Party B is 0.55, and the reliability of devices from Party B is 0.8. Therefore, the probability of a device from Party B working for the warranty period is 0.55 * 0.8 = 0.44.

Step 3: Calculate the total probability of the device working for the warranty period.

To calculate the total probability, we need to consider both cases: purchasing a device from Party A and purchasing a device from Party B. Since these events are mutually exclusive, we can simply add the probabilities calculated in Step 1 and Step 2.

The total probability of the device working for the warranty period is 0.315 + 0.44 = 0.755.

Therefore, the probability that the purchased device will work for the warranty period is 0.755.

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