Math challenge - Mega Millions white ball range

Reply #5

Orange71 — Thu, 11 May 2023 23:54:37 GMT

Indeed, that is correct. 54 is the Mode with 375700 combinations out of 12103014 total possible combinations, or around 3.1%.

Reply #4

Wavepack — Tue, 09 May 2023 07:24:19 GMT

Thanks for posting that counting proof.

Looking at a plot of the pdf, the mode looks to be 54.

Reply #3

Orange71 — Sat, 06 May 2023 16:30:19 GMT

Solution:

Consider a range, r , as a random variable representing a specific member of the set R = {5,6,7...,70}. The probability of each r is not the same and must be calculated in turn. However, we recognize that all possible random combinations for r = 5,...,70 must add up to 70 C 5 = 12103104. This is the fixed denominator in calculating the probability of each r in succession.

Now let's consider the numerators, which are the numbers of all possible random combinations for each r. In... [ More ]

Reply #2

Orange71 — Fri, 05 May 2023 18:30:47 GMT

It can be solved analytically to exact values. No need for a Monte Carlo simulation. If you are interested in the solution I can post it.

Reply #1

Wavepack — Fri, 05 May 2023 02:27:12 GMT

The possible values are {5, 6, ..., 70}. Not sure how to solve analytically. Could simulate to get the answer.

Math challenge - Mega Millions white ball range

Orange71 — Sat, 29 Apr 2023 15:17:29 GMT

There are 70 white (main) balls in Mega Millions. The player chooses 5 balls from 1 to 70 (or opts for a Quick Pick to randomly choose the same). Define R (for range) as max ball - min ball + 1 . For example, if the player chooses the balls {1, 2, 3, 4, 5}, then R = 5. Now consider the case where the balls are chosen randomly, such as a Quick Pick or lottery drawing for the winning numbers. R is now a random variable, and the set of all possible values of R is {1, 2, 3, ... , 70}.

Suppose th... [ More ]