Project #24599 - Law of Large Numbers

An insurance policy sells for $1200. Based on past data, an average of 1 in 125 policyholders will file a $10,000 claim, an average of 1 in 100 policyholders will file a $50,000 claim, and an average of 1 in 250 polictyholders will file a $80,000 claim. Find the expected value (to the company) per policy sold. If the company sells 10,000 policies, what is the expected profit or loss?

The expected value is-

The expected (profit or loss) is -

 

In a large casino, the house wins in its blackjack table with a probability of 51.8%. All bets at blackjack are 1 to 1-if you win, you gain the amount you bet; if you lose, you lose the amount you bet.

a. What is the expected value  to you of a single game? What is the house edge?

b. If you played 400 games of blackjack in an evening, betting $3 on each hand, how much should you expect to win or lose?

c. If patrons bet $4,000,000 on blackjack in one evening, how much should the casino expect to earn?

 

A sweepstakes posted the probabilites of winning each prize and the prize amounts as shown in the chart below. Suppose that one sweepstakes entry costs $1. Find the expected value of the winnings for any indivicual entry. Then state how much you can expect to win or lose if you spend $165 in entries. 

 

Prize            Probability

$1,000,000     1 in 100,000,001

$100,000        1 in 50,000,001

$1000             1 in 25,000,001

 

The expected value of the winnings for any individual entry is - 

If you spend $165 in entires, you can expect to (win/lose) -

 

When you give $5 for a bet in a casino game, there is a 252/495 probability that you will lose $5 and there is a 243/495 probability that you will make a net gain of $5 (If you win the casino gives you $5 and you get to keep your $5 bet, so the net gain is $5) What is the expected value? In the long run, how much do you lose for each dollar bet? 

Subject Mathematics
Due By (Pacific Time) 03/08/2014 11:59 pm
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