Question

Imagine that Alina's shower leaks and she calls the plumber. The plumber tells her that the problem is caused by either a leaky drain or a cracked shower pan, but never both. He also tells her that, in his experience, a leaky drain is the cause of the problem in about 90 % of cases. If he discovers that the drain is the problem, he can fix it for $ 250 . If he discovers that the shower pan is the problem, he must charge $ 2500 instead. What is the expected value of the repair price? Please round your answer to the nearest whole dollar.

Answer 1

The expected value of repair is $475

Explanation:

In this question, we are asked to calculate the expected value of repair price for a shower leak given the two possible causes, their prices and probabilities.

To calculate this, what we need to do is to multiply the probabilities by the individual amounts and add to each other.

For a leaky drain, there is a probability or chance of 0.9(90%) and the cost for this is $250. We proceed with the multiplication here.

Mathematically, the expected price due to leaky drain will be = probability of fault caused by leaky drain * amount for repairs if fault is caused by leaky drain

= 0.9 * 250 = $225

Now, for a shower pan problem, there is a probability of 0.1(10%) and the cost for this is $2,500. We also proceed with the multiplication here.

Mathematically, for a shower pan problem;

We have 0.1 * 2,500 = $250

The expected value of repair = leaky drain expected value of repair + shower pan expected value of repair = $250+$225 = $475