The Open Championship 2019: What will be W. Simpson and S. Garcia’s COMBINED SCORE on the Par 4 18th

Inputs To Solve

##### User Estimates #####

hole_18 = {'3':17,
           '4':93,
           '5':61,
           '6':7,
           '7':2}

print("The observed distribution of scores on hole 18 is: %s" % hole_18)

The observed distribution of scores on hole 18 is: {‘3’: 17, ‘4’: 93, ‘5’: 61, ‘6’: 7, ‘7’: 2}

## Inputs Defined in the Problem

strokes = 8
golfers = ['Simpson','Garcia']

Method to Solve

Enumrate all the possible combinations of observed scores and their respective probabilities for the 2 golfers on hole 18.
The probability that exactly 8 Strokes are recorded by Simpson and Garcia on hole 18 is the sum of the probabilities for all the outcomes where the total number of Strokes is exactly equal to 8.

import numpy as np
import pandas as pd

t=sum(hole_18.values())
for i in hole_18:
    hole_18[i] = hole_18[i]/t
 
y = np.array([(x,z) for x in hole_18.keys() for z in hole_18.keys()])
scores = pd.DataFrame(y)
scores.columns = golfers
scores = scores.convert_objects(convert_numeric=True)
scores['total_strokes'] = scores.sum(axis=1)

z = np.array([(x,y) for x in hole_18.values() for y in hole_18.values()])
probability = pd.DataFrame(z)
probability.columns = golfers
probability['p'] = probability.product(axis=1)

scores.head()

	Simpson	Garcia	total_strokes
0	3	3	6
1	3	4	7
2	3	5	8
3	3	6	9
4	3	7	10

probability.head()

	Simpson	Garcia	p
0	0.094444	0.094444	0.008920
1	0.094444	0.516667	0.048796
2	0.094444	0.338889	0.032006
3	0.094444	0.038889	0.003673
4	0.094444	0.011111	0.001049

p = probability['p'][scores['total_strokes']==strokes].sum()

Solution

print("The probability that W. Simpson and S. Garcia's COMBINED SCORE on the Par 4 18 is 8 STROKES equals ~%s" % round(p,3))

The probability that W. Simpson and S. Garcia’s COMBINED SCORE on the Par 4 18 is 8 STROKES equals ~0.331

Posted on 7/19/2019