A company sells high fidelity amplifiers capable of generating 10, 25 and 50 W o

Question

A company sells high fidelity amplifiers capable of generating 10, 25 and 50 W of audio power. It has on hand 100 of the 10-W units, of which 15% are defective, 70 of the 25-W units with 10% defective, and 30 of the 50-W units with 10% defective. What is the probability that an amplifier sold from the 10-W units is defective? If each wattage amplifier sells with equal likelihood, what is the probability of a randomly selected unit being 50 W and defective? What is the probability that a unit randomly selected for sale is defective?

Explanation / Answer

a) as it is given that probabilty that an amplifier sold from the 10W unit is defective =0.15.

b) as they have equally likelihood of 3 categories each one has probabilty of 1/3

hence probabilty that unit being 50 W and defective =(1/3)*(0.1) =0.033

c)total units =100+70+30 =200

probabilty that a randomely selected sale is defective =P(that it is 10 W and defective)+P(that it is 25 W and defective)+P(that it is 50 W and defective) =(100/200)*0.15+(70/200)*0.1+(30/200)*0.1=0.125

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