Hole in One Probability
I am having a discussion with my golfer friends,
and we have different opinions about the odds for getting a hole
in one. Do they change once you get a hole in one? In other
words, what are the odds that a person can get two holes in one
vs one in a lifetime of golf?
Probability of events depends upon whether or not the probability of
event(2) does/or does not depend upon the probability of event(1).
An example where the probability of the events are connected is if
the golfer keeps practicing on the same hole again and again under
the same conditions of wind, temperature, fatigue, etc. This is
usually not the case. The "normal" game of golf involves different
holes and different conditions over which the golfer has no control.
So the events are not correlated. If the probability of getting a
hole-in-one is P1 and the probability of getting a hole-in-one on
the second hole is P2 and the events are not correlated, then the
probability of getting two holes in one is P1 x P2 which makes the
cumulative probability P12 = P1xP2 very small since both P1 and P2
are individually quite small.
Getting one hole-in-one does not make it any harder to get another
hole-in-one. Probability applies only to what has not yet happened. I do
not know the general probability of getting a hole-in-one, but let us ASSUME
it is 0.1% (i.e. 0.001 out of one). This is the probability of getting a
hole-in-one sometime in the future. (I will now use HIO as shorthand for
The probability does NOT mean that you will get on HIO for every 1000 games
played. In means that for every individual game played, regardless of
previous games, the odds of getting a HOI are 0.001, or 1 in 1000. Consider
having 999 white marbles and 1 black marble. If you mix them up, close your
eyes, reach inn and grab one marble. The odds are 0.001 that it will be the
black marble. If you leave the first white marble out and try again, then
probability increases to 1 out of 999. This is not how most probabilities
happen. What you do is put the first white marble back in and shake the
marbles up again. Any effect of the previous event is "erased".
The probability of getting two HIOs in the future would be (0.001)*(0.001).
This is 0.000001, or 0.0001%. Once you get the first HIO, getting the
second is no less likely than the first. This is because the first HIO is
now definite. It DID happen. The probability of a definite event is 100%,
or 1. Once you have for a fact gotten the first HIO, the probability of
getting a second one as well becomes (0.001)*(1)=0.001. In most cases, past
events do not make future events more difficult. The only time it does
matter is when the past event has changed the circumstances or changed the
rules. If getting the first HIO required the golfer to use damaged clubs
for the rest of his life, then getting the second HIO would be more
Dr. Ken Mellendorf
Illinois Central College
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Update: June 2012