Q:

Assume the two races are independent of one another. What is the the expected value?

Accepted Solution

A:
Answer: D) $41,562.50Step-by-step explanation:You can narrow your choics to A or D based on your knowledge that expected value is a weighted average of the possible outcomes. The expected value cannot be higher than the highest possible outcome, nor can it be lower than the lowest. The probability of two wins is ... 0.25·0.35 = 0.0875so the expected value of that outcome is $100,000·0.0875 = $8,750__The probability of one win is the sum of the probabilities of a win in the first race followed by a loss, and a loss in the first race followed by a win. The expected value of that outcome is ... (0.25·0.65 +0.75·0.35)·$60,000 = $25,500__The probability of two losses is ... 0.75·0.65 = 0.4875Though this is the most probable outcome, it is nearly the same as the probability of one win. The expected value of two losses is ... $15,000·0.4875 = $7,312.50The expected value of all the outcomes is the sum of these, ... $8750 +25500 +7312.50 = $41,562.50 . . . . . . matches selection D