Question

a company estimates that 0.9% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $50. if they offer a 2 - year extended warranty for $7, what is the companys expected value of each warranty sold?

Explanation:

Step1: Calculate the probability of failure and success

The probability of failure \(p = 0.9\%=0.009\), and the probability of success \(q = 1 - p=1 - 0.009 = 0.991\)

Step2: Calculate the expected value formula

The formula for expected value \(E(X)\) is \(E(X)=x_1p_1 + x_2p_2\).
If the product fails, the company's net gain is \(7 - 50= - 43\) (they receive \(7\) for the warranty but have to pay \(50\) for replacement). If the product does not fail, the company's net gain is \(7\) (they just receive the warranty money).

Step3: Substitute values into the formula

\(E(X)=(-43)\times0.009+7\times0.991\)

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Answer:

\(6.55\)