SOLUTION: Tickets for a raffle cost $15. There were 758 tickets sold. One ticket will be randomly selected as the winner, and that person wins $1300. For someone who buys a ticket, what is t

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Question 1200362: Tickets for a raffle cost $15. There were 758 tickets sold. One ticket will be randomly selected as the winner, and that person wins $1300. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)?
If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer rounded to two decimal places.
Expected Value = $
(PLEASE EXPLAIN) I do not understand, and it would be a lot if the steps were shown.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Tickets for a raffle cost $15. There were 758 tickets sold.
One ticket will be randomly selected as the winner, and that person wins $1300.
For someone who buys a ticket, what is the Expected Value (the mean of the distribution)?
If the Expected Value is negative, be sure to include the "-" sign with the answer.
Express the answer rounded to two decimal places.
Expected Value = $
(PLEASE EXPLAIN) I do not understand, and it would be a lot if the steps were shown.
~~~~~~~~~~~~~~~~~~~~~ 

Formally, you need to calculate the probability of getting the winning ticket, first.

This probability is  ,  since there are 758 tickets, in all, 
and only one is the winning.


Then you should multiply this probability by the winning amount of $1300

     = 1.715039578  dollars.


It is the mathematical expectation to win.


But they ask you about another value: about the expected NET value of the distribution.


To get this value, you should subtract $15 from 1.715039578, and you will get

    1.715039578 - 15 = -13.285 dollars (rounded).


It is your ANSWER.


        In other words, the machine spreads evenly the amount of $1300 among 758 tickets 
        and then you pay $15 from your pocket to this machine for its work.
        The change of the balance in your pocket after that operation is called "the net expectation".

Hope now you do understand everything.

The sign "-" means that you lose money CATASTROPHICALLY in this game.

So, do not play this way . . .


////////////////////


It is why you should learn Math very insistently:

        - it teaches you how to live; what to do and HOW to do it; and what not to do.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer = -13.28

========================================================================
Explanation:

X = net winnings

If a person wins $1300, and the ticket costs $15, then they walk away with $1285 (since 1300-15 = 1285)
In short: X = 1285 is one possibility.

The other outcome is when X = -15 to represent cases when the person doesn't win anything. Even worse: They lost $15.

There's 1 winning ticket out of 758 total
1/758 represents the probability of winning, so it's tied to X = 1285
In other words, P(X) = 1/758 when X = 1285

1-(1/758) = 757/758 is the probability connected to X = -15

To summarize so farOften it's handy to organize this information into a table
XP(X)
12851/758
-15757/758

Use of spreadsheet software is strongly recommended.

We'll then form a new column labeled X*P(X)
This is where we multiply each X with its corresponding P(X) value
XP(X)X*P(X)
12851/7581285/758
-15757/758-11355/758

Then we add up the results of that new column.
(1285/758)+(-11355/758)
(1285-11355)/758
-10070/758
-13.2849604221636
-13.28

That is the approximate expected value. More specifically, it's the approximate expected net winnings.
It means that the average person expects to lose about $13.28

-----------------------------------------

Another approach:

The previous method used the standard textbook approach with expected value problems. That template outline being:
  1. Construct the probability distribution table of each X and P(X)
  2. Compute X*P(X) for each row.
  3. Add up each X*P(X) value
For this second approach, imagine a single person buying all 758 tickets at $15 each.
In total, they spent 758*15 = 11370 dollars.

That means they are down this amount.
We write -11370 to indicate this loss.

But this player is guaranteed to win the prize of $1300 because they bought all the tickets.
Their net winnings is -11370+1300 = -10070
They're still down a considerable amount of money.

Divide this net loss over the number of tickets to determine the average loss per ticket.
-10070/758 = -13.2849604221636 = -13.28

Therefore, this player lost on average approximately $13.28 per ticket.

Hopefully you notice that these calculations are very similar to the previous section's calculations.
The numbers haven't changed too much.

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