A product is made out of three independent components that are connected togethe

Question

A product is made out of three independent components that are connected together in some way ( We don’t care how right now)
When component 1 is made, it will be cracked with probability 0.23
When component 2 is made, it will be cracked with probability 0.24.
When component 3 is made it will be cracked with probability 0.26.
If all three components are cracked, the product must be thrown away. If all three components are NOT cracked, the product can be sold at a premium price. Otherwise, the product can be sold, but with an ordinary profit margin.
A. Calculate the probability that the product will be scrapped.
B. Calculate the probability the product will be sold at a premium.
C. Calculate the probability that the product will be sold with an ordinary profit margin.
D. Write an expression for the probability that when 1000 products are made, less than 3 % will be scrapped.

Explanation / Answer

A. You left out the information about the circumstances under which a product is scrapped. If the product is scrapped when all three components are bad, the probability would be: (0.23)(0.24)(0.26) = 0.014 B. 1-(0.77)(0.76)(0.74) = 0.567 C. Again, it's not clear when a product is scrapped vs. sold at ordinary profit margin. Assuming that the product is sold at ordinary profit margin when only 1 or 2 components is bad, then this would be: 1-[0.567+0.014] = 0.419 D. binomcdf(1000,0.014,29) = 0.99988. again, this assumes item is scrapped if all three are bad

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