   SEARCH HOME Math Central Quandaries & Queries  Question from Robert: There are four (4) par 3's at a specific 18 hole course. One member has the honor of making a Hole-in-one on all four par 3's. It has taken him 8 years to do it! How does one go about computing the odds of this TREMENDOUS accomplishment? Respectfully, Robert Robert,

You can make a decent guess if your club has records.

Can you estimate the number of rounds played per year over the last 1 year, say? (Maybe 150 per day for the number of days the course is open for play.) And then do you know the number of holes in one on each of those holes during the last 1 year?

If you do, then you can calculate like this:

• an estimate of the probability (chance) of a hole in 1 on par three number k in any given year is $p_k = \mbox{ (# holes in 1) divided by (number of rounds).}$

• the probability of not getting a hole in 1 on par 3 number k in a given year is $(1 -p_k)$

• the probability of getting at least one hole in 1 on par three number k in 8 years is $q_k = \left(1 - (1-p_k)^8 \right)$ ($(1-p_k)^8$ means $(1 - p_k)$ raised to the 8th power).

• the probability of getting at least one hole in 1 on each of the 4 par 3's in 8 years is $q_1 \times q_2\times q_3 \times q_4.$

It should be a really small number.
--Victoria     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.