Expected Value Answers

Johnny is challenged to a single-player game with an expected value of 1. Which statement below is true?

Two students devised a game called “3 Pennies & 2 Nickels.” Each player will choose to play the pennies or the nickels. In each round, the players will flip all their coins on the table and record how many heads and tails they have. The table below includes the point scheme.Point Values for “3 Pennies & 2 Nickels”Penny PointsNickel PointsAll pennies heads: –2Both nickels heads: –2At least one of each: +3One of each: +5All pennies tails: –2Both nickels tails: –2Alyssa wants to play the game. Choose the statement below that is correct in all aspects.

The marketing club at school is opening a student store. They randomly survey 50 students about how much money they spend on lunch each day. What is the expected value for a student to spend on lunch each day? Student Lunch SurveyNumber of StudentsDollars Spent on Lunch Each Day2 $101$812$623$58$44$3

Given the spinner below in which all regions are equal, which of the following point scales would result in a favorable game?

Two black chips and three red chips are put into a bag. Two points are awarded for each black chip drawn, and one point is lost for each red chip drawn. What is the expected value for each round if there are two draws per round and the chips are replaced after each draw?

A company makes a $5 profit on each non-faulty product it sells. Approximately 2% of the products manufactured are faulty, with no way to discover which ones are faulty before delivery. If replacement-and-repair costs for the faulty products are $100 each, what is the profit per item?

A cafeteria purchases milk from one of three providers each week, depending on what other items need to be purchased. The probability of shopping at each store and the cost of one gallon of milk are shown in the table below. Probability and Milk Cost by StoreStoreProbability Milk Cost per GallonA30%$3.00B10%$3.50C60%$2.75The cafeteria should budget $

An investor has an opportunity to invest in three companies. She researched each company and collected the information in the table below. Which company would provide the best investment?Probability of Profit and Loss by CompanyCompanyLoss, Probability of LossProbability to Break EvenProfit, Probability of ProfitA$24,000, 16%50%$10,000, 34%B$12,000, 32%40%$21,000, 28%C$6,000, 23%17%$5,000, 60%

Which statement below correctly depicts the expected value of a fair game?

A trucking company operates in three regions of the country. The table below depicts the probability that each company truck is in the region and the fuel prices per gallon. What amount should the company budget on average for a gallon of fuel across its operations? Round your answer to the nearest cent.Probability and Fuel Cost by RegionRegionProbability in RegionFuel Cost per GallonSoutheast20%$3.10Southwest30%$3.50California50%$4.05