please check my solution..probability/ expected values.

[Meital]

hello, I am trying to work the following problem, but i know i am doing something wrong since my answer doesn't make sense.

Suppose we roll a die repeatedly until we see each number at least once. Let R be the number of rolls required. fin ER ( the mean value of R).

The way I did it is:

Each number has a probability p of being shown, and q of not. p = 1/6, and q = 1-p = 5/6.

ER = p + pq + pq^2 + pq^3 + pq^4 + pq^5 for the first # that will show

+ pq + pq^2 + pq^3 + pq^4 + pq^5 for 2nd one

+ pq^2 + pq^3 + pq^4 + pq^5 for 3rd one

+ pq^3 + pq^4 + pq^5 for 4th one

+ pq^4 + pq^5 for 5th one

+ pq^5 for 6th one

but when finding the value i got an answer close to 2 which doesn't make sense, will you please tell me what i am doing wrong..this is urgent please let me know asap

[Jake712]

What exactly are you looking for?

The number of rolls Required in order to see all of the numbers is 6 because there are six sides and theoretically one could roll a dice and never see all of the numbers therefore I think it is possible to find the mean value of the number of rolls required. According to my logic, you are trying to find the mean of 6 through infinity. However, my class has just started probability, therefore, I know very little and am probably confused.

 

So ignore my rambling

[Meital]

The procedure is as follows:

You roll the die the first time and you see a number, then now you are trying to get all the other numbers to appear at least once. So you roll again, if it is the same number you had the first time, you will roll again to get one of the 5 other numbers, otherwise, you will roll again to see the rest 4 numbers. So I don't think the way you solved it is correct. I know every side has a probability of 1/6 to appear, but this doesn't mean that every time you roll you will get a different number. I still need help

[5614]

in the end its down to chance.

 

so by chance i could roll it 6 times and get all 6 numbers

 

or by chance i may roll it 5 times and get numbers 1-5 and then have to roll it a few hundred times to get the 6... (just by chance)

 

it is all chance - i dont think that there is an exact number as the chances of that number being right are probably very small!