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Forum index » Science and Technology » Math » Recreational
Calculating golf odds
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Johnny
science forum beginner


Joined: 29 Mar 2005
Posts: 20

PostPosted: Wed Oct 12, 2005 1:22 pm    Post subject: Calculating golf odds Reply with quote
Hello, all.

I'm hoping to get some help in thinking about how to calculate a
probability.

What is the p that a golfer will make 11 holes-in-one in a single round
of 18 holes?

I realize this sounds ridiculous, but there is a reason for this
question. You may go to http://barelybad.com/words1.htm and search for
"October 12, 2005" to see it.

The only information we have is that the p of getting three holes-in-one
is 1 in 2 trillion.

How can I translate that statistic into the p of 11 such holes-in-one?

Thanks.
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Lynn Kurtz
science forum Guru


Joined: 02 May 2005
Posts: 603

PostPosted: Wed Oct 12, 2005 5:59 pm    Post subject: Re: Calculating golf odds Reply with quote
On Wed, 12 Oct 2005 08:22:46 -0500, "Johnny" <barelybad@hotmail.com>
wrote:

Quote:
Hello, all.

I'm hoping to get some help in thinking about how to calculate a
probability.

What is the p that a golfer will make 11 holes-in-one in a single round
of 18 holes?

I realize this sounds ridiculous, but there is a reason for this
question. You may go to http://barelybad.com/words1.htm and search for
"October 12, 2005" to see it.

The only information we have is that the p of getting three holes-in-one
is 1 in 2 trillion.

How can I translate that statistic into the p of 11 such holes-in-one?

Thanks.


Given that a typical 18 hole course doesn't have 11 par 3 holes, the
probability of getting 11 holes in one on such a course is zero.

--Lynn
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Bill McCray
science forum beginner


Joined: 18 May 2005
Posts: 44

PostPosted: Wed Oct 12, 2005 6:13 pm    Post subject: Re: Calculating golf odds Reply with quote
On Wed, 12 Oct 2005 08:22:46 -0500, "Johnny" <barelybad@hotmail.com>
wrote:

Quote:
Hello, all.

I'm hoping to get some help in thinking about how to calculate a
probability.

What is the p that a golfer will make 11 holes-in-one in a single round
of 18 holes?

I realize this sounds ridiculous, but there is a reason for this
question. You may go to http://barelybad.com/words1.htm and search for
"October 12, 2005" to see it.

The only information we have is that the p of getting three holes-in-one
is 1 in 2 trillion.

How can I translate that statistic into the p of 11 such holes-in-one?

Although we know this isn't true, assume the probability of getting a
hole-in-one is equal for all of the holes. Let P be this probability.
Then the probability of getting a hole-in-one on N specific holes and
not on the rest is

P^N x (1 - P)^(18-N)

The number of sets of N specific holes out of 18 is

18!/(N! x (18-N)!)

Therefore, the probability of getting a hole-in-one on any N of 18
holes is

P^N x (1 - P)^(18-N) x 18!/(N! x (18-N)!)

Let's call that Q(N).

Now you are given that Q(3) = 1/(2 trillion). From that you can
compute P and, given P, you can compute Q(11).

Since "billion" has more than one interpretation internationally, I
suspect "trillion" does, too, so I didn't try to write out the number
for "2 trillion".

Bill
__________
Swap first and last parts of username and ISP for address.
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Pavel314
science forum addict


Joined: 29 Apr 2005
Posts: 78

PostPosted: Sun Oct 16, 2005 1:42 am    Post subject: Re: Calculating golf odds Reply with quote
"Johnny" <barelybad@hotmail.com> wrote in message
news:a1fcd$434d0e2d$407e5bd5$5202@EVERESTKC.NET...
Quote:
Hello, all.

I'm hoping to get some help in thinking about how to calculate a
probability.

What is the p that a golfer will make 11 holes-in-one in a single round
of 18 holes?

I realize this sounds ridiculous, but there is a reason for this
question. You may go to http://barelybad.com/words1.htm and search for
"October 12, 2005" to see it.

The only information we have is that the p of getting three holes-in-one
is 1 in 2 trillion.

How can I translate that statistic into the p of 11 such holes-in-one?

Thanks.

Do you have the probability of getting a hole in one? That seems to be the
key to this problem; once you have that factor, the rest would fall into
place.
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Bill McCray
science forum beginner


Joined: 18 May 2005
Posts: 44

PostPosted: Sun Oct 16, 2005 10:19 pm    Post subject: Re: Calculating golf odds Reply with quote
On Sat, 15 Oct 2005 21:42:22 -0400, "Pavel314"
<Pavel314@NOSPAM.comcast.net> wrote:

Quote:
"Johnny" <barelybad@hotmail.com> wrote in message
news:a1fcd$434d0e2d$407e5bd5$5202@EVERESTKC.NET...
Hello, all.

I'm hoping to get some help in thinking about how to calculate a
probability.

What is the p that a golfer will make 11 holes-in-one in a single round
of 18 holes?

I realize this sounds ridiculous, but there is a reason for this
question. You may go to http://barelybad.com/words1.htm and search for
"October 12, 2005" to see it.

The only information we have is that the p of getting three holes-in-one
is 1 in 2 trillion.

How can I translate that statistic into the p of 11 such holes-in-one?

Thanks.

Do you have the probability of getting a hole in one? That seems to be the
key to this problem; once you have that factor, the rest would fall into
place.

As I said in an earlier post, given the probability of getting three
holes-in-one out of eighteen holes (which we are) and making some
assumptions, we can calculate the probability of getting a hole-in-one
on any single hole.

One possible assumption: The probability of making a hole-in-one on
all holes is the same. Given a standard golf course, this isn't true,
but it might be on a par-three golf course.

Another one: The probability of making a hole-in-one for each of the
four par-three holes on a standard golf course* is the same; for the
other 14 holes, it's zero. (Well, I guess an eagle might catch the
ball in the air and drop it into the hole. Would that count as a
hole-in-one?) Anyway, under this assumption, it's impossible to make
eleven holes-in-one out of eighteen holes.

* I haven't played much golf, but I think it's normal to have two
par-three holes in each nine.

And we also have to make an assumption of what is meant by 2 trillion.
A billion in the U.S. is a thousand million, but in Britain it was
traditionally a million million. I think generally the british have
now changed to the U.S. terminology, so maybe it's safe to assume that
a trillion is a million million.

Bill
__________
Swap first and last parts of username and ISP for address.
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