Rework problem 22 from section 3.4 of your text, involving defective replacement

Question

Rework problem 22 from section 3.4 of your text, involving defective replacement printer cartridges. Assume that the store stocks 30 percent brand A, 50 percent brand B, and the rest are brand X. Assume further that 5 percent of brand A, 15 percent of brand B, and 30 percent of brand X will not provide the number of pages advertised. A customer buys a cartridge at random.

If the customer returns the cartridge because it does not provide the number of pages advertised, what is the probability that the cartridge was brand X?

Explanation / Answer

P(does not provide the number of pages advertised)=P(brand A and does not provide the number of pages advertised)+P(brand B and does not provide the number of pages advertised)+P(brand X and does not provide the number of pages advertised)

=0.3*0.05+0.5*0.15+0.2*0.3=0.15

hence P(cartridge was brand X given does not provide the number of pages advertised)

=P(brand X and does not provide the number of pages advertised)/P(not provide pages advertised)

=0.2*0.3/0.15 =0.4

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