a fair die is rolled 8 times. what is the probability that the point 5 occurs at least 7 times?

Answer 1

This probability is equal to the sum of the probabilities that 5 occurs 7 or 8 times. Assuming we're talking about a six-sided die, the odds are 1:6^8 that 5 occurs 8 times. There are considerably more ways in which 5 could occur only 7 times. Each of the 8 dice could assume one of the 5 other values, so there are 40 combinations of rolls with 7 5's. The total number of possible outcomes is still 6^8, so the final probability is 41:6^8 = 0.0000244 = 0.00244%. The odds are not very good.