Exploring Probability of Coin Toss in 2D and Euclidean Planes

In summary, the conversation is about a minor project on dimensions and probability involving a coin of diameter d being randomly tossed onto a rectangular cartesian plane. The question is to find the probability of the coin not intersecting any line with equations in the form of y=mx+c or (x/a)+(y/b)=1. The person is starting with a 2-D figure and may expand to the euclidean plane if they get a proper answer. The need to restrict the area being worked with is also mentioned. There is a discussion about the intercept form of a line in regards to part (b) of the question.
  • #1
Mr.IITIAN007
20
0
Well I am doing a minor project on dimensions and probablity.Please friends try this out:-----------

A coin of diameter d is tossed randomly onto the rectangular cartesian plane .
What is the probablity that the coin does not intersect any line whose equation is of the forms :-------
(a) y=mx+c
(b) (x/a)+(y/b)=1

I am trying first with 2-D figure but if I get a proper answer I can find for euclidean plane too.
 
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  • #2
(b) is also a line. I assume you mean to square the x and y.

Obviously, you need to somehow restrict the area you're working with. You cannot use the entire euclidean plane as there exists no uniform distribution over it.
 
  • #3
Ziox,You are right about your point on euclidean plane.I have not yet thought about that.But buddy, (b) is the intercept form of a line which cuts off intercepts a and b from x and y-axis respectively.Have you tried the (a) part ?
 

FAQ: Exploring Probability of Coin Toss in 2D and Euclidean Planes

What is probability?

Probability is a measure of the likelihood of a certain event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

How is probability calculated?

In the context of coin tosses in 2D and Euclidean planes, probability can be calculated by dividing the number of desired outcomes by the total number of possible outcomes. For example, if we want to find the probability of getting heads on a coin toss, we divide the number of ways to get heads (1) by the total number of outcomes (2), resulting in a probability of 1/2 or 0.5.

What is the difference between 2D and Euclidean planes?

2D planes refer to a flat surface with only two dimensions: width and length. Euclidean planes, on the other hand, refer to a geometric space with three dimensions: width, length, and height. In the context of coin tosses, 2D planes are used to represent the two possible outcomes (heads or tails), while Euclidean planes are used to show the different positions a coin can land on when tossed.

How does the number of coin tosses affect probability?

The more coin tosses that are performed, the closer the actual results will be to the expected probability. This is known as the Law of Large Numbers, which states that as the number of trials increases, the average outcome will approach the expected probability.

Why is exploring probability of coin tosses important?

Exploring probability of coin tosses allows us to better understand the concept of probability and its application in real-life situations. It also helps us make more informed decisions and predictions based on the likelihood of certain events occurring.

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