PGA Rocket Mortgage Classic - 2nd Rd: What will be Tyrrell Hatton’s SCORE on Holes 16-18?
4:30PM
12 Stokes or Fewer
13 Strokes or More
Inputs to Solve
##### User Estimates #####
hole_16 = {'3':5,
'4':186,
'5':222,
'6':38,
'7':1}
hole_17 = {'3':312,
'4':210,
'5':202,
'6':28,
'7':1}
hole_18 = {'3':14,
'4':212,
'5':208,
'6':18}## Inputs Defined in the Problem
strokes = 12
golfers = ['Hatton16','Hatton17','Hatton18']Method to Solve
- [1] Enumrate all the possible combinations of observed scores and their respective probabilities on the 3 holes.
- [2] The probability that 12 Strokes or Fewer (p_under12) is recorded by Hatton on holes 16-18 is the sum of the probabilities for all the outcomes where the total number of Strokes is 12 or less.
import numpy as np
import pandas as pd
t=sum(hole_16.values())
for i in hole_16:
hole_16[i] = hole_16[i]/t
t=sum(hole_17.values())
for i in hole_17:
hole_17[i] = hole_17[i]/t
t=sum(hole_18.values())
for i in hole_18:
hole_18[i] = hole_18[i]/t
y = np.array([(w,x,z) for w in hole_16.keys() for x in hole_17.keys() for z in hole_18.keys()])
scores = pd.DataFrame(y)
scores.columns = golfers
scores = scores.apply(pd.to_numeric)
scores['total_strokes'] = scores.sum(axis=1)
z = np.array([(w,x,y) for w in hole_16.values() for x in hole_17.values() for y in hole_18.values()])
probability = pd.DataFrame(z)
probability.columns = golfers
probability['p'] = probability.product(axis=1)
scores| Hatton16 | Hatton17 | Hatton18 | total_strokes | |
|---|---|---|---|---|
| 0 | 3 | 3 | 3 | 9 |
| 1 | 3 | 3 | 4 | 10 |
| 2 | 3 | 3 | 5 | 11 |
| 3 | 3 | 3 | 6 | 12 |
| 4 | 3 | 4 | 3 | 10 |
| … | … | … | … | … |
| 95 | 7 | 6 | 6 | 19 |
| 96 | 7 | 7 | 3 | 17 |
| 97 | 7 | 7 | 4 | 18 |
| 98 | 7 | 7 | 5 | 19 |
| 99 | 7 | 7 | 6 | 20 |
100 rows × 4 columns
probability| Hatton16 | Hatton17 | Hatton18 | p | |
|---|---|---|---|---|
| 0 | 0.011062 | 0.414343 | 0.030973 | 1.419648e-04 |
| 1 | 0.011062 | 0.414343 | 0.469027 | 2.149753e-03 |
| 2 | 0.011062 | 0.414343 | 0.460177 | 2.109192e-03 |
| 3 | 0.011062 | 0.414343 | 0.039823 | 1.825262e-04 |
| 4 | 0.011062 | 0.278884 | 0.030973 | 9.555326e-05 |
| … | … | … | … | … |
| 95 | 0.002212 | 0.037185 | 0.039823 | 3.276112e-06 |
| 96 | 0.002212 | 0.001328 | 0.030973 | 9.100310e-08 |
| 97 | 0.002212 | 0.001328 | 0.469027 | 1.378047e-06 |
| 98 | 0.002212 | 0.001328 | 0.460177 | 1.352046e-06 |
| 99 | 0.002212 | 0.001328 | 0.039823 | 1.170040e-07 |
100 rows × 4 columns
## [2]
p_under12 = probability['p'][scores['total_strokes']<=strokes].sum()Solution
print("The probability Tyrrell Hatton's SCORE on Holes 16-18 is 12 Strokes or Less is ~ %s" % round(p_under12,3))The probability Tyrrell Hatton's SCORE on Holes 16-18 is 12 Strokes or Less is ~ 0.341Info
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import sys
print(sys.version)3.6.5 (v3.6.5:f59c0932b4, Mar 28 2018, 16:07:46) [MSC v.1900 32 bit (Intel)]