0

your friend decides to roll a die repeatedly to analyze whether the probability of a six on each flip is 1/6. He rolls the die 10 times and observes six 7 times. He concludes that the probability of a six for this die is 7/10=0.7. A. Your friend claims that the die is not balanced, since the probability is not 0.166666667. What's wrong with your friend's claim? B. If the probability of rolling a six is 1/6, what would you have to do to ensure that the cumulative proportion of sixes falls very close to 1/6?

haley cartrette
  • 1
  • Frequentist probability is a reasonable approach to estimating probabilities. The problem with your friend's logic is that $10$ trials is an inadequate substitute for an infinite number of trials. His claim does have the benefit of being easily reproducible (and easily disproven). – David Diaz Oct 31 '19 at 23:11
  • Another problem with the logic: lets assume that true probabilities are always (# of successes)/(# of trials) for any number of trials. Roll a die once. What needs to be the outcome to verify that $P(six) = 0.7$? – David Diaz Oct 31 '19 at 23:19
  • Let us imagine the following better situation. In a Las Vegas casino there is once a day a big experiment published in the newspapers. They have the same game, but published. In some week you get an Monday early in the morning a mail, watch, "there will be a 6 today". And indeed, there was a 6. Well, no problem, but early on Thu. also, "there will be a 6 today". And indeed, this was the case, and this happened every day. Next week, the mail changes, "there will be a 6 today, do you want to bet $1000$$?!*" This must hurt you to understand the problem, things simply happen, so it is... – dan_fulea Oct 31 '19 at 23:21
  • ... a special situation, maybe the mail sender sends billions of mails in the world. An experimentally described situation may be strange, but with some probability this still happens. Exactly so also in the OP. The friend had a hard time to find the 10 rolls with seven times the $6$. Then he asked the question. And even if we have an unbalanced case... there is one world where we model, this is probability, and one world where we estimate, this is statistics. People mix them, but these are "different mathematical games". – dan_fulea Oct 31 '19 at 23:26

0 Answers0