# Average Money per Day from a probability that stacks each day and give income over 5 days.

Each day there is a chance (lets say for this example 15%) i get 500 euros over 5 days (this means 100 euro each day for the next 5 days that this will happen) How can i calculate the Average Income per Day for this probability? My thinking was :

1st day :IncomeChance * Amount /5 -> 0,15 *500 /5 = 15euro

2nd day : 2 * IncomeChance * Amount /5 -> 2* 0,15 *500 /5 = 30 euro

...

5th day : IncomeChance * Amount -> 0,15 *500 /5 = 75 euro

and from 5th day and over this stays as IncomeChance * Amount.

Can i include all the above in one result?

thank you

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The problem needs better definition. You have a 15% chance of receiving 100 euros on day 1. What about day 2? You have a 15% chance of getting 100 because you won on day 1, but is there another chance of winning on day 2? May you only win on day 2 if you lost on day 1? This needs to be specified before a calculation can be made. –  Ross Millikan Nov 19 '12 at 14:05
On each day you can win those 500 euros with 15% chance. but those 500 euros you dont get them in the same day you win but you get them over the next 5 days..so in day one if you win you get 100 euros each day for the next 5 days including the day you won. the second day you might win 500 more that will go over the next 5 days etc etc. i hope it will be more understandable now. –  Excadrix Nov 19 '12 at 14:38
I got that there is another chance on day 2, but if you win day 1 can you win day 2 (and get 200 euros) or don't you get a chance until day 6? –  Ross Millikan Nov 19 '12 at 15:03
no you can win on day 2 too.. they are not depentable... –  Excadrix Nov 19 '12 at 15:30
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## 1 Answer

If there is a new draw every day, for each day after day 4 you receive 100 euro for each win in the preceding five, so your expectation is $5$ (tries) $\cdot 100$ (payout per win) $\cdot 15\%$ (chance of win)$=75$. For the first four days, decrease $5$ as you don't get that many tries, but in the long run you can ignore the startup transient.

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ok so is any expression that will compare the above situation with a similar which everything will be the same except the period the money are paid? what i mean is it the same thing that get the money over 5 days and over 10 days or over 20 days? cause as i think it the best thing it would be if i get all the money in the same day i win which gives the same amount (75) as it will be over 5 days (the only difference is the first 4 days) how can i include those 4 days in the equation? –  Excadrix Nov 19 '12 at 17:11
@Excadrix: the long term expectation doesn't reflect how fast the money is paid. It is no different from being given 100 euros today or 1 euro per day for 100 euros. For the first four days, your expectation is 15, 30,45,60 euros. –  Ross Millikan Nov 19 '12 at 17:16
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