A batch of 1000 piston rings manufactured in an engine manuf

A batch of 1000 piston rings manufactured in an engine manufacturing facility contains 40% defective. Two piston rings are randomly selected from the batch, one at a time, without replacement. If Ei denotes the event that the i the piston ring selected is defective (i=1, 2), determine the values, P(E1) and P(E2).

Solution

X - no of defects in the 1000 piston rings is binomial

p = 0.40 and n = 1000

P(E1) = Prob that first one is defective

= 0.40

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P(E2) = Prob that second one is defective

= P(first one good and second one defective)+P(first one def and second one defective)

= 0.60(0.40) + (0.40)(0.40)

= 0.40