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The Random Problem (Posted on 2004-02-09) Difficulty: 4 of 5
Suppose there are 20 problems on the site the Sunday evening a user looks at the site the first time. She doesn't read the newest problem of the day, but instead ONLY reads problems that come up on the "Random Problem" page. She reads 5 random problems each day, always in the evening. The only problem is she can see the same problem more than once.

The other problem is problems continue to come in from the infinite queue. Two per week day and one per weekend.

What is the probability she will have read all the problems after her next Sunday evening check? What is the probability she will have read all the problems after the Sunday evening after that?

Note: The problems displayed when you click on "Random Problem" are independent of each other. There isn't anything to make sure that you are getting five different problems if you click on random problem five times.

See The Solution Submitted by Gamer    
Rating: 4.1429 (7 votes)

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A solution | Comment 7 of 8 |
I'm assuming on this that the one problem that comes in per Sunday has already come in. So she has 1/(20^5) chance of reading a different problem each time she clicks on "Random Problem". I'm also assuming that she reads the new problems each day AFTER the two new problems have come in each day. Which means the next day (Monday) she will have 1/(20^5)*1/(22^5) chance of reading a new problem each time she clicks on "Random Problem". This will go progressive each day ending up in an equation something like this, 1/(20^5)*1/(22^5)*1/(24^5)*1/(26^5)*1/(28^5)*1/(30^5)*1/(31^5)*1/(32^5) chance of reading all the different problems by the next Sunday evening.
  Posted by Vincent on 2004-03-09 13:39:52
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