Question

Станок 30 % времени обрабатывает деталь А и 70 % - деталь В. При обработке детали А он простаивает 10 % времени, а детали В - 15 %. Какова вероятность застать станок простаивающим? Найти вероятность, что станок, который застали простаиваю¬щим, находится в режиме обработки детали В.

Answer 1

По формуле полной вероятности получаем
Р=0,3*0,10+0,7*0,15=0,135
по формуле Байеса получаем
Р=0,7*0,15/0,135=0,777

Answer 2

Problem Analysis

We are given that a machine spends 30% of its time processing part A and 70% of its time processing part B. Additionally, the machine is idle 10% of the time when processing part A and 15% of the time when processing part B. We need to find the probability of finding the machine idle and the probability of finding the machine processing part B when it is idle.

Probability of Finding the Machine Idle

To find the probability of finding the machine idle, we need to calculate the combined idle time for both part A and part B.

The machine spends 30% of its time processing part A and is idle 10% of the time when processing part A. Therefore, the idle time for part A is 30% * 10% = 3%.

Similarly, the machine spends 70% of its time processing part B and is idle 15% of the time when processing part B. Therefore, the idle time for part B is 70% * 15% = 10.5%.

To find the combined idle time, we add the idle time for part A and part B: 3% + 10.5% = 13.5%.

Therefore, the probability of finding the machine idle is 13.5%.

Probability of Finding the Machine Processing Part B when Idle

To find the probability of finding the machine processing part B when it is idle, we need to calculate the idle time specifically for part B.

The machine spends 70% of its time processing part B and is idle 15% of the time when processing part B. Therefore, the idle time for part B is 70% * 15% = 10.5%.

To find the probability of finding the machine processing part B when it is idle, we divide the idle time for part B by the combined idle time: 10.5% / 13.5% ≈ 0.778.

Therefore, the probability of finding the machine processing part B when it is idle is approximately 0.778 or 77.8%.

Conclusion

- The probability of finding the machine idle is 13.5%. - The probability of finding the machine processing part B when it is idle is approximately 0.778 or 77.8%.

Please note that the above calculations are based on the given information and assumptions made.