suppose you are planning to buy a computer. the computer comes with a one - year warranty, but you can…

suppose you are planning to buy a computer. the computer comes with a one - year warranty, but you can purchase a warranty for an additional year of $24.95. your research indicates that in the second year, there is a 1 in 20 chance of incurring a major repair that costs $180 and a probability of 0.15 of a minor repair that costs $65.\nis it worth purchasing the additional year warranty? why or why not?

suppose you are planning to buy a computer. the computer comes with a one - year warranty, but you can purchase a warranty for an additional year of $24.95. your research indicates that in the second year, there is a 1 in 20 chance of incurring a major repair that costs $180 and a probability of 0.15 of a minor repair that costs $65.\nis it worth purchasing the additional year warranty? why or why not?

Answer

Explanation:

Step1: Calculate probability of major repair

The probability of a major repair is $\frac{1}{20}= 0.05$.

Step2: Calculate expected cost of repairs

The expected - value formula for the cost of repairs $E(X)$ is $E(X)=\sum_{i}x_ip_i$. Here, $x_1 = 180$ (cost of major repair) with $p_1=0.05$, $x_2 = 65$ (cost of minor repair) with $p_2 = 0.15$, and the probability of no - repair $p_3=1-(0.05 + 0.15)=0.8$. $E(X)=180\times0.05+65\times0.15+0\times0.8$ $E(X)=9 + 9.75+0$ $E(X)=18.75$.

Step3: Compare expected cost with warranty cost

The cost of the additional - year warranty is $24.95$, and the expected cost of repairs in the second year is $18.75$. Since $18.75<24.95$.

Answer:

It is not worth purchasing the additional year warranty because the expected cost of repairs in the second year ($18.75$) is less than the cost of the additional - year warranty ($24.95$).