Question

An LG Dishwasher, which costs $950, has a 25% chance of needing to be replaced in the first 2 years of

purchase. A two-year extended warrantee costs $112.10 on a dishwasher. Assume the dishwasher is replaced in
the first 2 years.
a) Write out the probability distribution for the value of the extended warranty.
Make sure you enter your X values from smallest to largest.
X
P(X)
b) What is the expected value of the extended warranty?
Round final answer to 2 decimal places and write the units in the cond box.

Answer 1

The probability distribution for the value of the extended warranty is X = $112.10, P(X) = 0.25 and X = $0, P(X) = 0.75. The expected value of the extended warranty is $28.03.

Step-by-step explanation:

To write out the probability distribution for the value of the extended warranty, we need to calculate the probability of the dishwasher being replaced in the first 2 years and the cost of the extended warranty.

The probability of the dishwasher being replaced in the first 2 years is 0.25, and the cost of the extended warranty is $112.10.

Therefore, the probability distribution for the value of the extended warranty is as follows:

1. X = $112.10, P(X) = 0.25
2. X = $0, P(X) = 0.75

To find the expected value of the extended warranty, we multiply each value of X by its corresponding probability and sum the products.

Expected value = ($112.10 * 0.25) + ($0 * 0.75) = $28.03.