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Expert: - 10/21/2008


Question
A manufacturer of dishwashers uses electric pumps from the 3 suppliers P,Q and R, in the ratios 5:3:2, respectively. Of the pumps from the supplier P, 8 percent fail during the warranty period. The corresponding figures for the pumps supplied by Q and R are 10 percent and 5 percent respectively.

A) For one of the dishwashers chosen at random, calculate the probability that its pumps

(i) is supplied by Q and fails during the warranty period.
(ii) fails during the warranty period
(iii) is supplied by R. given that it fails during the warranty period.

B)For a random sample of three pumps supplied to the manufacturer, calculate the probability that no two come from the same supplier.

C) For two pumps chosen at random from those that fail during the warranty period , calculate the probability that they come from the same supplier.


Thank you on your help, i realy realy realy apriciate it

Answer
Name, supplies, fail
P, 0.5, 0.08
Q, 0.3, 0.10
R, 0.2, 0.05

A)
i) given Q, failure is 0.10

ii) take the sum of the product of the variables in front of P, Q, and R.  Example: P is 0.5*0.08. Do the same for the others and add them up.

iii) Take each the value computed for R last time (0.2*0.05) and divide by the values obtained for the sum of P, Q, and R.

B) This would mean that they all came from different suppliers.  Three pumps, three suppliers, so the value 0.9*0.3*0.2.

C) They could both come from P and Q, P and R, or R and Q.
Take the value from Aii and multiply in three pairs (PQ, PR, and QR).

For PQ, this would be (0.5*0.08)(0.3*0.10).  Do the same for PR and QR, then add up these values.

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