7C Concept Check

An insurance company knows that the average cost to build a new California subdivision is $100,00 and that in any particular year there is a 1 in 50 chance of a wildfire destroying all the homes in the subdivision. Based on these data and assuming the insurance company wants a positive expected value when it sells policies, what is the minimum that the company must charge for fire insurance policies in this subdivision?

$2000 per year

You know a shortcut to work that uses side streets instead of the freeway. Most of the time, the shortcut takes 5 minutes off the driving time by freeway. However, about once in every ten trips, an accident blocks traffic on the shortcut, with the result that the trip takes 20 minutes longer than it would by freeway. In terms of the amount of time the shortcut saves, what is the expected value of the shortcut?

(5 minutes x 0.9)

Consider a lottery with 100 million tickets in which each ticket has a unique number. Each ticket sold for $1, and one ticket is drawn for a single prize of $75 million (and no other prizes). The expected value of a single ticket is

- $0.25

Suppose that the probability of a hurricane striking Florida in any single year is 1 in 10 and that this probability has been the same for the past 100 years. Which of the following is implied by the law of large numbers?

Florida has been hit by close to (but not necessarily exactly) 10 hurricanes in the past 100 years.

A $1 slot machine at a casino is set so that it returns 97% of all the money put into it the form of winnings, with most of the winnings in the form of huge of but low-probability jackpots. What is your probability of winning when you put $1 in this slot machine?

It cannot be calculated from the given data, but it is certainly quite low.

Consider the slot machine described in Question 9. Which statement is true if patrons have put $10 million into this slot machine?

The casino's profit has been close to $300,000.

You are betting on a game in which each bet has an expected value of -$0.40. This means that

if you play the game many times, on average you will lose about $0.40 per game.

Cameron is betting on a game in which the probability of winning is 1 in 4. He's won ten games in a row, so he decides to double his bet on the eleventh game. This strategy shows

poor logic, as he has a 75% chance of losing the double bet

Cameron is betting on a game in which the probability of winning is 1 in 4. He's lost ten games in a row, so he decides to double his bet on the eleventh game. This strategy shows

poor logic, as he has a 75% chance of losing the double bet.

Consider the lottery ticket described in Question 2. If you were to spend $1 million to purchase 1 million lottery tickets, the most likely result would be that

you would lose your entire $1 million