Chapter PIII, Problem 43RE

To determine

To Explain: the number of strokes may it really take on the basis of provided assumptions

Explanation of Solution

there are advised that a to play a par-4 hole tees off, striking the ball in the fairway, striking the green with a tee shot. It's not likely that the first putt will go in, however the second putt should. Interpreted as follows, there is need to decide number of strokes it would really take:

-- 70 percent of the time, the tee shot strikes the fairway.

-- This first approach shot lands 80 percent of the time from of the fairway on the green, but otherwise just 40 percent of the time.

-- Corresponding straight shots land 90 % of the time mostly on green.

-In 20 percent of the time, a first putt goes. 90 percent of the time, and ensuing puns go in.

In order to determine the golfer 's score, we must use a simulation. Based on the provided probabilities, we can randomly generate starting from 1 to 100 to every shot and compute the score. For example, if number is equal to or lower than 70, the tee shot would reach the fairway.

Here are the outcomes of ten arbitrary simulations:

Simulations	Number of Strokes
1	5
2	4
3	5
4	6
5	5
6	4
7	4
8	4
9	5
10	3

Now, we can calculate the average of the strokes in the ten simulations by adding the ten strokes and dividing by the number 0f simulations.

$\begin{array}{c}\text{Average}\text{=}\frac{\text{\#}\text{of}\text{Strokes}}{\#of\text{Simulations}}\end{array}$

  $\begin{array}{c}\text{=}\frac{5+4+5+6+5+4+4+4+5+3}{10}\end{array}$

  $\begin{array}{c}=4.5\end{array}$

Therefore, this would require 4.5 strokes to finish the hole on average.