applied probability

2009-10-22 8:24 am

我知可能長左d....
The completion time of a building depends on whether the carpenters and plumbers working on its construction go on strike. The probability of delay in completion are @, 8@, 16@ and 1 if
neither go on strike,
if the plumbers alone go on strike,
if the carpenters alone go on strike and
if both go on strike, respectively, where 0<@<1/16.
The plumbers have a probability $ of going on strike. If the plumbers are on strike, the carpenters have a probability 3$ of also being on strike, where 0<$<1/6. Similarly, if the carpenters are on strike, the plumbers have a probability 6$ of also being on strike. Determine the probability of delay in completing the building.

回答 (1)

Prof. Physics

2009-10-23 4:04 am

✔ 最佳答案

P(plumber on strike) = $

P(carpenters on strike│plumber on strike)

= P(carpenters on strike and plumber on strike) / P(plumber on strike)
So, 3$ = P(carpenters on strike and plumber on strike) / $

P(carpenters on strike and plumber on strike) = 3$^2

P(carpenters and plumber not on strike) = 1 - 3$^2

P(plumber on strike│carpenters on strike)

= P(carpenters on strike and plumber on strike) / P(carpenters on strike)

P(carpenters on strike) = 3$^2 / 6$ = $/2

P(carpenters alone on strike)

= P(carpenters on strike) - P(carpenters and plumber on strike)

= $/2 - 3$^2

P(plumber alone on strike)

= P(plumber on strike) - P(carpenters and plumber on strike)

= $ - 3$^2

Therefore, the probability of delay

= 3$^2 (1) + (1 - 3$^2)(@) + ($/2 - 3$^2)(16@) + ($ - 3$^2)(8@)

= 3$^2 + @ - 3$^2@ + 8$@ - 48$^2@ + 8$@ - 24$^2@

= 3$^2 + @ + 16$@ - 75$^2@

參考: Physics king

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