Question 921014: Probabilities
1) Take a standard deck of 52 cards and shuffle it repeatedly. How many
possible ways are there to draw seven cards from this deck? How many possible ways are there to draw 11 cards? How many possible ways are there to draw 13 cards?
2)Rory is a foreman at a metal pressing factory. Unfortunately, 20% of the
time, he forgets to turn off the pressing machine before going home for the day. If Rory turns off the machine, then it cools down over night and the proportion of defective units the next morning is only 6%. However, if he forgets to turn the machine off, then it does not cool down and the next morning, the proportion of defective units is 35%. If you are
driving in to the factory in the morning and don’t know whether he turned the machine off or not, and this morning we are going to produce 100 units, how many do you expect will be defective? If you get to the factory and find the machine still on, now how many units do you expect will be defective?
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website! 1) 52C7 =133,784,560 , 52C11 = 60,403,728,840 , 52C13 = 635,013,559,600
2)p(forgets to turn off) = .20
p(def, turned off) = .06
p(def, left on) = .35
....
P(def..not knowing) = P(def-ON 0r def-OFF) = .80*.06 + .20*.35 = .118 0r 12 def
P(def| ON) = .35
.35*100 = 35 expected to be defective
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