Probability between 2 people in golf

[akhanijow]

Hi,
I am having some issues with this problem. Any help is much appreciated!

There are two people competing in a golf match, Person A and Person B. For a hole with a par-3 rating, Person A has the following probabilities of getting the ball in the hole in the designated number of strokes:
Strokes 1 2 3 4 5 6 7
0.00 0.09 0.68 0.21 0.02 0.00 0.00

Person B has the following probabilities:

Strokes 1 2 3 4 5 6 7
0.00 0.13 0.67 0.17 0.02 0.00 0.00



I am trying to calculate the probability that Person B wins, the probability that they tie, and the probability that Person A wins.

I know that once the probability that person A (or B) is found, the probability that the other person wins is just 1-p, but I am having trouble figuring out how to get the probabilities. Any help would be great, thanks!

 

[tjackson3]

Two things:

1.) Once you find the probability p that person A wins, the probability that person B wins is not necessarily 1-p. That is only the case if the probability that A and B tie is zero, which is not so. Now, if you find the probability p that person A wins and the probability r that they tie, the probability that person B wins is 1-p-r.

2.) How do you define a person winning in this context? Use that definition to get you closer to what you want to calculate. Person A wins if their number of strokes is less than the number of strokes of person B. Also, their scores are mutually independent. My thought (although it's been awhile since I've had probability, so this may be unnecessarily complicated and tedious) would be to start with: what is the probability that A gets one stroke AND B gets two strokes? OR B gets three strokes? etc.