Thread: Expected Value

Confused in this section.. help appreciated..

If anyone can help with this... is there not a calculator function that will help??

Two examples:

In a lottery 3,000,000 tickets are sold at a dollar a piece. Out of these 12,006 are drawn at random without replacement and awarded prizes of 12,000 $25, 4 $10,000 prize, 1 $50,000 prize and 1 $200,0000 prize. What is the expected value of 1 per week.

Next one,

In a state lottery a three-digit integer is selected randomly. If a player bets $1, on a number, the payoff is $500 minus $1 paid for ticket. Let X equal the payoff of -1 - 499 and find E(X)


Just a heads up I may need help on Bernoulli next.

Originally Posted by skyslimit

Confused in this section.. help appreciated..

If anyone can help with this... is there not a calculator function that will help??

Two examples:

In a lottery 3,000,000 tickets are sold at a dollar a piece. Out of these 12,006 are drawn at random without replacement and awarded prizes of 12,000 $25, 4 $10,000 prize, 1 $50,000 prize and 1 $200,0000 prize. What is the expected value of 1 per week.

Hi there

You should consider each prize and the probability of recieving thast prize.

For $25: probabilty = 12,000/3,000,000

For $10,000: probabilty = 4/3,000,000

For $50,000: probabilty = 1/3,000,000

For $200,000: probabilty = 1/3,000,000

and finally if you don't win the prize is $-1 so

For $-1: probabilty = (3,000,000-12,006)/3,000,000 = 2,987,994/3,000,000

Now multiply each return by its respective probabilty and sum the products together. This is the expected value.

Very Helpful, thank you.

On the second, I understand I must simply multiply the odds of of winning and losing (+- one dollar) by the winnings and loss. However, I can't seem to remember the odds of a random 3 digit integer... could it be simply would. Obvously 3! is too small... would it be, however, 27 * 27 * 27??

Originally Posted by cjmac87

Very Helpful, thank you.

On the second, I understand I must simply multiply the odds of of winning and losing (+- one dollar) by the winnings and loss. However, I can't seem to remember the odds of a random 3 digit integer... could it be simply would. Obvously 3! is too small... would it be, however, 27 * 27 * 27??

With the second question I read it as there are 900 three digit numbers i.e (100, 101, 102, ..... ,997,998,999) as i would not include numbers like 001 or 023, because these are really 1 or 2 digit numbers (maybe or maybe not for this exercise!?)

So

If you are including the numbers I left out befroe then the queation would be:

So