Calculating Probability of Golf Ball Landing Near Hole on 4th Hole

In summary, the conversation discusses a word problem and a finite difference problem. The word problem involves calculating the probability of a ball landing within 2 feet of the center of a circular green on a golf course. The finite difference problem involves finding the nth-order differences for a given function. The conversation provides a solution for the word problem and a question for the finite difference problem. The probability of the ball landing in the hole is determined to be 1/900.
  • #1
woodworker101
19
0
I have a word problem and then a finite difference problem.

You are playing golf on the 4th hole of your favorite course. The green on this hole is circular with a radius of 20 yards. If the hole is located at the exact center of the green, what is the probablility that the ball will randomly fall within 2 feet of the center of the hole?

finding Finite differences - nth order differences

f(x) = 2x^2 -5x^2 -x

I don't know how to start it and how to get the answer. Thanks for the help.
 
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  • #2
Assuming the ball will always land on the green, just find the area of the green and the area of the 2-foot circle, then compare them (in a ratio). (Remember to keep your units consistent).
 
  • #3
I got 900 to 1. Is the correct or even close.
 
  • #4
Yes. Actually, you don't even need to calculate the areas themselves to compare them. The hole has radius 2 feet and the green 60 feet- a ratio of 1 to 30. Since area depends on the square of linear distance the area will have ratio 1 to 900.
The probability that a ball that lands randomly on the green will land in the hole is 1/900.

As for f(x) = 2x^2 -5x^2 -x, I see a function (although I would write f(x)=
-3x^2- x) but I see no finites differences and I certainly don't see a question!
What is the problem?
 
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  • #5
The question is for the finite difference is: Show that the nth-order differences for the given function of deghree N are nonzero and constant. such as f(x) = 2x^3 - 5x^2 - x
 
  • #6
I am curious how you got ur 900 to 1 ratio. Would the probably also be 1 % too.
 

Related to Calculating Probability of Golf Ball Landing Near Hole on 4th Hole

1. How do you calculate the probability of a golf ball landing near the hole on the 4th hole?

The probability of a golf ball landing near the hole on the 4th hole can be calculated by dividing the number of favorable outcomes (balls landing near the hole) by the total number of possible outcomes (all possible landing spots for the ball). This can be represented as a fraction or a percentage.

2. What factors affect the probability of a golf ball landing near the hole on the 4th hole?

The factors that can affect the probability of a golf ball landing near the hole on the 4th hole include the golfer's skill level, the distance from the tee to the hole, the terrain and obstacles on the course, and weather conditions such as wind and rain.

3. Can the probability of a golf ball landing near the hole on the 4th hole be accurately calculated?

While it is possible to calculate the probability of a golf ball landing near the hole on the 4th hole, it may not always be accurate due to the unpredictable nature of the sport. There are many variables that can affect the outcome of a golf shot, making it difficult to accurately predict where the ball will land.

4. How can understanding probability help improve a golfer's game?

Understanding probability can help a golfer make more strategic decisions on the course. By knowing the likelihood of a ball landing near the hole on the 4th hole, a golfer can choose the best club and aim for a spot with a higher probability of success.

5. Is there a way to increase the probability of a golf ball landing near the hole on the 4th hole?

While there is no guaranteed way to increase the probability of a golf ball landing near the hole on the 4th hole, practicing and improving one's skills can lead to more accurate shots and therefore, a higher chance of landing near the hole. Additionally, taking into account factors such as wind and terrain can also help increase the probability of a successful shot.

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