PGA Travelers: How many BIRDIES will V. Hovland, J. Rose and T. Finau record on HOLES 7 and 8?

Inputs to Solve

2020 Course Stats

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

p_bird = [22/378, 30/378]

count = 7
for p in p_bird:
    print("The probability that a golfer BIRDIES hole " + str(count) + " is %s" % round(p,3))
    count +=1

The probability that a golfer BIRDIES hole 7 is 0.058
The probability that a golfer BIRDIES hole 8 is 0.079

## Inputs Defined in the Problem

total_birdies = 1
holes = ['Hovl_7','Rose_7','Finau_7','Hovl_8','Rose_8','Finau_8']

Method to Solve

[1] Enumerate all the possible combinations BIRDIES and NON-BIRDIES being scored on holes 7-8 for 3 golfers (2^6 combinations).
[2] The probability that 1 BIRDIE is recorded by V. Hovland, J. Rose and T. Finau on HOLES 7 and 8 is the sum of the probabilities for all the outcomes where the total number of BIRDIES is exactly equal to 1 (p_1).

## [1]

import numpy as np
import pandas as pd

outcomes = (1,0)

y = np.array([(a,b,c,d,e,f) for a in outcomes for b in outcomes for c in outcomes 
              for d in outcomes for e in outcomes for f in outcomes])
birdies = pd.DataFrame(y)
birdies.columns = holes
birdies['total_birdies'] = birdies.sum(axis=1)

x = np.array([(a,b,c,d,e,f) for a in (p_bird[0],1-p_bird[0]) for b in (p_bird[0],1-p_bird[0]) 
              for c in (p_bird[0],1-p_bird[0]) for d in (p_bird[1],1-p_bird[1]) 
              for e in (p_bird[1],1-p_bird[1]) for f in (p_bird[1],1-p_bird[1])])
probability = pd.DataFrame(x)
probability.columns = holes
probability['p'] = probability.product(axis=1)

birdies

	Hovl_7	Rose_7	Finau_7	Hovl_8	Rose_8	Finau_8	total_birdies
0	1	1	1	1	1	1	6
1	1	1	1	1	1	0	5
2	1	1	1	1	0	1	5
3	1	1	1	1	0	0	4
4	1	1	1	0	1	1	5
…	…	…	…	…	…	…	…
59	0	0	0	1	0	0	1
60	0	0	0	0	1	1	2
61	0	0	0	0	1	0	1
62	0	0	0	0	0	1	1
63	0	0	0	0	0	0	0

64 rows × 7 columns

probability

	Hovl_7	Rose_7	Finau_7	Hovl_8	Rose_8	Finau_8	p
0	0.058201	0.058201	0.058201	0.079365	0.079365	0.079365	9.855553e-08
1	0.058201	0.058201	0.058201	0.079365	0.079365	0.920635	1.143244e-06
2	0.058201	0.058201	0.058201	0.079365	0.920635	0.079365	1.143244e-06
3	0.058201	0.058201	0.058201	0.079365	0.920635	0.920635	1.326163e-05
4	0.058201	0.058201	0.058201	0.920635	0.079365	0.079365	1.143244e-06
…	…	…	…	…	…	…	…
59	0.941799	0.941799	0.941799	0.079365	0.920635	0.920635	5.619258e-02
60	0.941799	0.941799	0.941799	0.920635	0.079365	0.079365	4.844188e-03
61	0.941799	0.941799	0.941799	0.920635	0.079365	0.920635	5.619258e-02
62	0.941799	0.941799	0.941799	0.920635	0.920635	0.079365	5.619258e-02
63	0.941799	0.941799	0.941799	0.920635	0.920635	0.920635	6.518339e-01

64 rows × 7 columns

## [2]

p_1 = probability['p'][birdies['total_birdies']==total_birdies].sum()

Solution

print("The probability that V. Hovland, J. Rose and T. Finau record 1 BIRDIE on HOLES 7 and 8 is ~ %s" % round(p_1,3))

The probability that V. Hovland, J. Rose and T. Finau record 1 BIRDIE on HOLES 7 and 8 is ~ 0.289

Info

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email: krellabsinc@gmail.com
twitter: @KRELLabs

import sys
print(sys.version)

3.6.5 (v3.6.5:f59c0932b4, Mar 28 2018, 16:07:46) [MSC v.1900 32 bit (Intel)]

Posted on 6/26/2020

	Hovl_7	Rose_7	Finau_7	Hovl_8	Rose_8	Finau_8	total_birdies
0	1	1	1	1	1	1	6
1	1	1	1	1	1	0	5
2	1	1	1	1	0	1	5
3	1	1	1	1	0	0	4
4	1	1	1	0	1	1	5
…	…	…	…	…	…	…	…
59	0	0	0	1	0	0	1
60	0	0	0	0	1	1	2
61	0	0	0	0	1	0	1
62	0	0	0	0	0	1	1
63	0	0	0	0	0	0	0

	Hovl_7	Rose_7	Finau_7	Hovl_8	Rose_8	Finau_8	total_birdies
0	1	1	1	1	1	1	6
1	1	1	1	1	1	0	5
2	1	1	1	1	0	1	5
3	1	1	1	1	0	0	4
4	1	1	1	0	1	1	5
…	…	…	…	…	…	…	…
59	0	0	0	1	0	0	1
60	0	0	0	0	1	1	2
61	0	0	0	0	1	0	1
62	0	0	0	0	0	1	1
63	0	0	0	0	0	0	0

	Hovl_7	Rose_7	Finau_7	Hovl_8	Rose_8	Finau_8	total_birdies
0	1	1	1	1	1	1	6
1	1	1	1	1	1	0	5
2	1	1	1	1	0	1	5
3	1	1	1	1	0	0	4
4	1	1	1	0	1	1	5
…	…	…	…	…	…	…	…
59	0	0	0	1	0	0	1
60	0	0	0	0	1	1	2
61	0	0	0	0	1	0	1
62	0	0	0	0	0	1	1
63	0	0	0	0	0	0	0