Probability of a given number of a set of random numbers

In summary, the probability of getting a specific number from a set of random numbers depends on the size of the set and the number of times the specific number appears. This can be calculated by dividing the number of times the specific number appears by the total number of numbers in the set. The probability can change if the set size or the number of times the specific number appears changes. The size of the set can also affect the probability, with larger sets generally having a smaller probability. However, there is no limit to the probability of a specific number in a set of random numbers, but as the size of the set increases, the probability becomes more predictable.
  • #1
Dragonfall
1,030
4

Homework Statement


Each week you receive a random number {1,...,n}. You may receive the same number more than once. Each number has 1/n probability of being sent to you. What is the expected amount of time until you receive the number 6?

Homework Equations


I'm not sure what to use here.

The Attempt at a Solution


The probability of receiving any number for the first time at the kth week should be .
 
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  • #2
Try computing the expectation value of k.
 
  • #3
I did, I get n, where everyone else seems to get n-1.
 
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