EXPECTED VALUES: E(X) = å X i P(X i ) What is the expected value of a lottery ti

Question

EXPECTED VALUES:                  E(X) = å XiP(Xi)

What is the expected value of a lottery ticket where there are only ten chances in a million of winning the grand prize of $25 Million?

You have been offered a chance to purchase a lottery ticket with a 10% chance of making $1000; 20% chance of making $100; and 70% chance of making $0. The price of the ticket is $20. Should you buy it? Why?

You have been offered a business deal. You estimate that there is a 5% chance of making $20,000; 25% chance of making $5000; 70% chance of making $100. How much should you be willing to pay for this deal?

Explanation / Answer

1. Probability of winning is 10/1million

Thus expected value is probability * prize = 10*25 or 250

2. This is 0.1*1000+0.2*100+0.7*0=120. Since the expected value is much higher than the price of ticket which is 20, you should buy it

3. 0.05*20000+ 0.25*5000+ 0.7*100= 1000+1250+70= 2320

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