Answer to Question #18329 in Statistics and Probability for Tony

Question

What is the probability of the same 2 individuals finishing 1st and 2nd in 2 consecutive contests that have 100 particpants each? To be more precise, individual 'A' finishes 1st in contest 1 and contest 2 while individual 'B' finishes 2nd in both contest 1 and contest 2. I calculate the probability as: 1/100 x 1/99 x 1/100 x 1/99. Is this correct?

Answer 1

Answer can be calculated as following:
1/100 x 1/99 x 1/100 x 1/99
Probability that individual A finishes first is 1 out of 100 it means 1/100, and probability that he finishes second is 1 out of 99 (because first place is already not available)
The same situation with individual B
But we need to take into consideration that we have two individuals in the systems, that’s why we need to multiply each profitability
1/100 x 1/99 x 1/100 x 1/99