I'm working on my Olympic Trials preview.
I've narrowed down the field to 4 studs whom I think will make the team. If they run well, they will beat everyone else in the field.
For simplicity sake, I decided to assume that if someone is in shape like these 4 that 75% of the time they will run good a marathon. Well what percent of the time do 2-3 or 4 of them run bad? I want to know because if 2 or more of them run a bad race, then my longshots have a chance.
Despite being a former HS math teacher, I am not going to try to figure it out myself. I've put the scenario into chatgpt and bard and get wildly different answers.
Initially I asked Bard and ChatGPT the following.
Calculate the odds of the following for me please. Four people are running the same race. Their odds of success are independent of each other. They each have a 75% of success. What percentage of the time do 2, 3 or 4 of them run a bad race?
ChatGPT said the "scenario you've described involves a binomial distribution" and said the answer was 30.86% whereas Bard said it was "32.42%".
I also asked the question in a different format and got wildly different results.
When I worded the problem as "Calculate the odds of the following for me please. I'm going to make 4 different investments. They each have a 75% of success. What percentage of the time do 2, 3 or 4 end up in failure?" Chat GPT said "approximately 30.86% of the time, 2, 3, or 4 out of the 4 investments will end up in failure" while Bard said the answer was just 5.08%.
So roughly what is the answer and please tell me why.