Quote:
Originally Posted by blueash
The odds of making a hole in one on a particular hole is one in how ever many holes are on that course. So for a nine hole course, it is one in nine (assuming you are going to make a hole in one on one of them, which is a given for the problem). Then the odds of the next one being on the same hole is one out of the same. We have to be careful because we have both 9 and 18 hole courses. So as long as his first hole in one was on hole one thru nine we can ignore that. So, he gets a hole in one on a hole 3. The chance it would be #3 is 1/9 The next time he gets a hole in one it is on an 18 hole course, so it is 1/18th likelihood to be on the same number. So that is 1/18 times 1/9 or 1/162 The next is on a nine hole course, which is 1/9 likelihood. So the odds of all three holes in one being the same 3 number hole is 1/1458 given your facts. Now, that it was a #3 ball, you multiply 1/1458 times 1/n with n= total number of choices for numbers on his balls (his golf balls). If he only plays with #1,2,3,4 then the chances for having used a #3 ball is 1/4, and he used it 3 times, so 1/4 times 1/4 times 1/4 or 1/64. We must assume that he does not subconsciously or intentionally always pull out a #3 ball when he gets to the third hole. So to have used a #3 ball on the same hole for 3 holes in one is now 1/1458 times 1/64 or 1/92,302 This ignores any factor for what are the odds he would even get a hole in one as that was not your question. All math done on a napkin, so please someone get out a calculator and make corrections as needed. If he has more or fewer options for ball numbers, the calculation of course changes.
|
You're assuming that all nine hole golf courses have nine par 3s or nine holes that are reachable in one shot. Most nine hole golf courses have two par threes. some have only one and a few may have three or more. In the Villages we get used to calling nine hole par three golf courses, "Executive Courses". An executive course can actually differ from a par three course.
Most executive course consist of a mixture of par 3s, 4s and sometimes even short par 5s. The difference is that they are usually shorter holes and may contain more par threes than the standard.
While there is no official definition of an executive course, I would say that a course where the par fours are in the 250-350 yard range, par threes under 200 yards and par fives under 475 could be defined as an executive course.
Executive courses and par three courses could be nine holes or eighteen holes. I have played several 18 hole par three courses.
So another factor that has to be looked at is how many courses have a par three (or a reachable par four for some people) as their third hole.
NGF gives all kinds of statistics for golf. I think that say that the odds of a hole in one on any par three hole by all players is 1:12000. There is a different ratio for professionals and still another for tour players. I think that they also have the odds of a player making more than one hole in one in a lifetime. Your husband's feat is incredibly rare. The only thing I have ever heard close to that was a player playing eighteen holes on a par 36 nine hole course made a hole in on the sixth hole twice in one round. That was in the millions to one range and I believe that three in a lifetime is in the millions to one and your husbands feat may be in the billions to one.