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Name: Daryl
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Question:
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?



Replies:
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.

Vince Calder


Daryl,

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 hole-in-one.)

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 difficult.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College



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