Probablity question

Athbi

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Jun 23, 2020
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7
Hello,
Let's say we are in a game of 10 players. Each player will have a word to describe his/her word to the other players without saying the word. In the game, there will be 10,000 unique words.

So, let's say there is a robot, and his task is to register every single word to its database. How many games would it take the robot to register all the 10,000 words to its database? By the way, the expected amount of words in each game is 10 since there are 10 players and each player will have a unique word IN A SINGLE GAME, however, a word may occur multiple times from previous games. In other words, for example, in game 1 your word is apple and player’s 2 word is banana and in game 2 your word is apple again. This is fine but what's not fine is in game one player 1 and 2 have the same word. Given the examples and the explanation, how many games would it take a robot to register all the 10,000 words?
 
Hello,
Let's say we are in a game of 10 players. Each player will have a word to describe his/her word to the other players without saying the word. In the game, there will be 10,000 unique words.

So, let's say there is a robot, and his task is to register every single word to its database. How many games would it take the robot to register all the 10,000 words to its database? By the way, the expected amount of words in each game is 10 since there are 10 players and each player will have a unique word IN A SINGLE GAME, however, a word may occur multiple times from previous games. In other words, for example, in game 1 your word is apple and player’s 2 word is banana and in game 2 your word is apple again. This is fine but what's not fine is in game one player 1 and 2 have the same word. Given the examples and the explanation, how many games would it take a robot to register all the 10,000 words?
To put this more clearly, you are apparently saying that on each trial (game), 10 different words are randomly chosen from a list of 10,000, and you want to know how many trials it will take for all 10,000 words to have appeared at least once.

I hope you recognize that the answer is indeterminate; it is possible that it will take only 1000 trials, and it is possible to take any number you imagine (though it becomes far less likely as you increase that number).

Presumably what you want is the expected number of trials. Is that a concept you are familiar with? Have you tried calculating it? Please show us your work:
 
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