Question

Рабочий обслуживает 3 станка. Вероятность того, что в течении смены станки будут исправны равна: для первого станка 0.6; для второго станка 0.7; для третьего 0.8. Найти вероятность того, что только два станка в течении смены будут исправны.

Answer 1

Ответ:

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Пошаговое объяснение:

Answer 2

Calculating the Probability of Two Machines Being Operational

To calculate the probability of exactly two out of three machines being operational during a shift, we can use the concept of binomial distribution. The formula for this is:

P(X=k) = (n choose k) * (p^k) * ((1-p)^(n-k))

Where: - n is the total number of trials (in this case, the number of machines) - k is the number of successful trials (in this case, the number of operational machines) - p is the probability of success for each trial (in this case, the probability of a machine being operational)

Applying the Formula

Using the given probabilities for each machine being operational: - For the first machine (p1 = 0.6) - For the second machine (p2 = 0.7) - For the third machine (p3 = 0.8)

We want to find the probability that exactly two out of three machines will be operational during the shift.

Calculating the Probability

Using the binomial distribution formula, we can calculate the probability for each combination of two machines being operational and then sum these probabilities to get the total probability.

For the first and second machines being operational: P(X=2) = (3 choose 2) * (0.6^2) * (0.4^1) For the first and third machines being operational: P(X=2) = (3 choose 2) * (0.6^1) * (0.4^2) For the second and third machines being operational: P(X=2) = (3 choose 2) * (0.7^1) * (0.3^2) Summing these probabilities will give us the total probability of exactly two out of three machines being operational during the shift.