Calculating a game's probabilities.

[goneforeign]

There's a weekly game at the London Guardian, the blog host poses a topic and the readers respond with pop music titles that fit the topic. Every week there are close to or over 1000 readers responding, many with multiple suggestions, in total there are over 2000 suggestions each week. When the game closes the host selects the 'best' 10 from the 2000. Recently there's been a rash of cases where single individuals have selected 3 of the final 10.
My question is, what is the probability of this happening and what's the probability of it happening 3 weeks out of six [with different readers]?
Or to ask it another way, what are the odds of this happening?

 

[mmwave]

I would approach this question by first defining the parameters and variables involved. In this case, the parameters would include the number of readers, the number of suggestions per reader, and the number of final selections made by the host. The variables would include the probability of a single reader being selected for the final 10, the probability of a single reader being selected for the final 10 three times in a row, and the overall probability of this happening.

To calculate the probability of a single reader being selected for the final 10, we can use the formula for calculating probability: P(event) = number of favorable outcomes / total number of possible outcomes. In this case, the number of favorable outcomes would be 10 (the number of final selections) and the total number of possible outcomes would be the total number of suggestions, which is 2000. Therefore, the probability of a single reader being selected for the final 10 is 10/2000, or 0.005 or 0.5%.

To calculate the probability of a single reader being selected for the final 10 three times in a row, we can use the same formula. However, since the events are independent (the selection of a single reader for the final 10 one week does not affect the selection the following week), we can multiply the probabilities together. Therefore, the probability of a single reader being selected for the final 10 three times in a row is (10/2000)^3, or 0.000000125 or 0.0000125%.

To calculate the overall probability of this happening, we would need to know the total number of readers participating in the game. Without this information, it is difficult to accurately calculate the overall probability. However, assuming that there are at least 1000 readers participating each week and that the readers change each week, the overall probability would be even lower.

In conclusion, the probability of a single individual being selected for the final 10 three times out of six weeks is very low, and the overall probability of this happening is even lower. However, without knowing the exact number of readers and other factors, it is difficult to accurately calculate the odds of this happening.