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PGA RBC Heritage - 2nd Rd: Will G. Woodland OR D. Johnson record a BIRDIE during Holes 6-7?


11:05AM
Yes: Either make at least 1 birdie on Holes 6-7
No: Neither make a birdie Holes 6-7


Inputs to Solve

2020 Course Stats
(data used up to start of 2nd round)

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

p_bird = [40/154, 14/154]

count = 6
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 6 is 0.26
The probability that a golfer BIRDIES hole 7 is 0.091

## Inputs Defined in the Problem

total_birdies = 0

Method to Solve

## [1]

import numpy as np
import pandas as pd


holes = ['6','6','7','7']
outcomes = (1,0)

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

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

birdies
6 6 7 7 total_birdies
0 1 1 1 1 4
1 1 1 1 0 3
2 1 1 0 1 3
3 1 1 0 0 2
4 1 0 1 1 3
5 1 0 1 0 2
6 1 0 0 1 2
7 1 0 0 0 1
8 0 1 1 1 3
9 0 1 1 0 2
10 0 1 0 1 2
11 0 1 0 0 1
12 0 0 1 1 2
13 0 0 1 0 1
14 0 0 0 1 1
15 0 0 0 0 0
probability
6 6 7 7 p
0 0.25974 0.25974 0.090909 0.090909 0.000558
1 0.25974 0.25974 0.090909 0.909091 0.005576
2 0.25974 0.25974 0.909091 0.090909 0.005576
3 0.25974 0.25974 0.909091 0.909091 0.055756
4 0.25974 0.74026 0.090909 0.090909 0.001589
5 0.25974 0.74026 0.090909 0.909091 0.015891
6 0.25974 0.74026 0.909091 0.090909 0.015891
7 0.25974 0.74026 0.909091 0.909091 0.158905
8 0.74026 0.25974 0.090909 0.090909 0.001589
9 0.74026 0.25974 0.090909 0.909091 0.015891
10 0.74026 0.25974 0.909091 0.090909 0.015891
11 0.74026 0.25974 0.909091 0.909091 0.158905
12 0.74026 0.74026 0.090909 0.090909 0.004529
13 0.74026 0.74026 0.090909 0.909091 0.045288
14 0.74026 0.74026 0.909091 0.090909 0.045288
15 0.74026 0.74026 0.909091 0.909091 0.452880
## [2]

p_0 = probability['p'][birdies['total_birdies']==total_birdies].sum()
p_BIRDIE = 1-p_0

Solution

print("The probability that G. Woodland OR D. Johnson record a BIRDIE during Holes 6-7 is ~ %s" % round(p_BIRDIE,3))

The probability that G. Woodland OR D. Johnson record a BIRDIE during Holes 6-7 is ~ 0.547




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 6/19/2020






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