The Open Championship 2019 - 1st Rd: How many PARS will J. Rahm, M. Kuchar AND P. Cantlay record on the Par 4 18th?

Inputs To Solve

##### User Estimates #####
p_par_18 = 21/(2+21+13+2)

print("The probability of a PLAYER scoring PAR on hole 18 is ~%s" % round(p_par_18,3))

The probability of a PLAYER scoring PAR on hole 18 is ~0.553

## Inputs Defined in the Problem
num_pars = 2
golfers = ['Rahm','Kuchar','Cantlay']

Method to Solve

Compute the probability of 0, 1 or 2 PARS being scored on hole 18 by the 3 golfers
The probability that 2 PARS are scored by the three golfers on hole 18 is the sum of the probabilities for all the outcomes where the total number of PARS is equal to 2.

import numpy as np
import pandas as pd

# Hole 18
p_other = 1 - p_par_18
prob = (p_par_18,p_other)
par = (1,0)
a = {}

y = np.array([(w,x,z) for w in par for x in par for z in par])
pars = pd.DataFrame(y)
pars.columns = golfers
pars['total_pars'] = pars.sum(axis=1)

x = np.array([(w,y,z) for w in prob for y in prob for z in prob])
probability = pd.DataFrame(x)
probability.columns = golfers
probability['p'] = probability.product(axis=1)

pars.head()

	Rahm	Kuchar	Cantlay	total_pars
0	1	1	1	3
1	1	1	0	2
2	1	0	1	2
3	1	0	0	1
4	0	1	1	2

probability.head()

	Rahm	Kuchar	Cantlay	p
0	0.552632	0.552632	0.552632	0.168775
1	0.552632	0.552632	0.447368	0.136627
2	0.552632	0.447368	0.552632	0.136627
3	0.552632	0.447368	0.447368	0.110603
4	0.447368	0.552632	0.552632	0.136627

p = round(probability['p'][pars['total_pars']==num_pars].sum(),3)

Solution

print("The probability that J. Rahm, M. Kuchar AND P. Cantlay record 2 PARS on the PAR 4 18th is ~%s" % p)

The probability that J. Rahm, M. Kuchar AND P. Cantlay record 2 PARS on the PAR 4 18th is ~0.41

Posted on 7/18/2019