有題Probability想請教大家幫幫忙.

[匿名]

2008-12-11 12:23 am

Records show that for every 100 items produced in a factory during the day shift,
2 are defective,and for every 100 produced during produced during the night,4 are defective.If during a 24 hour period, 2000 items are produced during the day and 800 during the night,what is the probability that an item picked at random from the 2800 produced during 24 hour period:

1) was produced in the day shift and was defective?
2) was produced in the night shift and was defective?
3) If a selected item is defective,what is the probability that it came from the day shift?

回答 (1)

Penguin

2008-12-11 1:04 am

✔ 最佳答案

P(defective of day shift) = 2/100=1/50
P(defective of night shift)=4/100=1/25
P(product fm day shift)=2000/2800=5/7
P(product fm night shift) = 800/2800=2/7

1) P(produced in the day shift and was defective)
=P(defective of day shift) *P(product fm day shift)
=1/50*5/7
=1/70

2) P(produced in the night shift and was defective)
=P(defective of night shift) *P(product fm night shift)
=1/25*2/7
=2/175

3)P(A|B)=P(A&B)/P(B)
P(product fm day shift given it is defective)
=P(produced in the day shift and was defective)/P(it was defective)
-->P(it was defective)=P(defective fm day shift)+P(defective fm night shift)
=(1/70)/(1/50+1/25)
=5/21

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