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November 27, 2014

November 27, 2014

Posted by **JM** on Friday, August 30, 2013 at 3:56pm.

Historical records indicate that 8% have defects in shafts only, 6% have defects in bushing only, and 2% have defects in both shafts and bushing. one of the hydraulic assemblies is selected randomly. What is the probability that the assembly has

a) a bushing defects?

b) a shaft or bushing defect?

c) exactly one of the two types of defects?

d) neither type of defect?

- probability -
**Graham**, Friday, August 30, 2013 at 7:40pmLet event s represent a Shaft defect and event b represent a Brushing defect.

The given probabilities are:

P(s ∩ ¬b) = 0.08

P(b ∩ ¬s) = 0.06

P(b ∩ s) = 0.02

Note: these are mutually exclusive

What you wish to find are:

a: Brushing defect.

P(b) = P(b ∩ ¬s) + P(b ∩ s)

b: Shaft or Brushing.

P(s U b) = P(b ∩ ¬s) + P(s ∩ ¬b) + P(b ∩ s)

c: Shaft and not Brushing OR Brushing and not Shaft

P((s ∩ ¬b) U (b ∩ ¬s)) = P(s ∩ ¬b) + P(b ∩ ¬s)

d: Not Shaft and not Brushing

P(¬s ∩ ¬b) = 1 - P(s U b)

- probability -
**bobpursley**, Friday, August 30, 2013 at 7:46pmGood post, Graham

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