What is the probability that they will form a triangle?

What is the probability that they will form a triangle?

1/4
If you break a stick at two points chosen uniformly, the probability the three resulting sticks form a triangle is 1/4.

Can the ropes of the 3 friends form a triangle?

Any three lengths will form a triangle.

Which of the three line segments can form a triangle?

If the length of any one side is greater than the sum of the length of the other two, the line segments cannot be used to create a triangle. It is possible to create a triangle using 3 line segments if the sum of the lengths of any two line segments is greater than the length of the third.

What is probability and statistics in math?

Probability and statistics are the mathematics used to understand chance and to collect, organize, describe, and analyze numerical data. Students need this mathematics to help them judge the correctness of an argument supported by seemingly persuasive data.

What is the probability that three random points on a unit circle would form a triangle that includes the center of the unit circle?

There is a 1/4 chance that point C will fall in place to create a triangle which contains the center of the circle.

How is Pascal’s triangle used in probability?

Pascal’s Triangle is an arithmetical triangle and is commonly used in probability. The row number to observe depends on how many objects there are in total. The number along the row represents the number of different combinations you can get, depending on how many objects you choose from the total.

What is the triangle inequality theorem in geometry?

triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.

Is it possible to draw a triangle with any 3 segment lengths Why do you think?

No; The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Which of the following lengths of 3 line segments can be the lengths of the side of a triangle?

Answer: (iii) 5 cm, 5 cm, 5 cm Can be the lengths of the sides of a triangle.

What is the probability that these three pieces can form a triangle?

The probability that these three pieces can form a triangle is 1 4 (coordinatize the stick form 0 to 1, call the breaking points x and y, consider the unit square of the coordinate plane, shade the areas that satisfy the triangle inequality edit: see comments on the question, below, for a better explanation of this).

How do you break a stick into two pieces?

The longest (or rather, not the shortest) is then broken into two. The stick is first broken into two pieces. A piece randomly selected with probability 1/2 is then broken into two. The stick is first broken into two pieces. A piece randomly selected with the probability proportional to its length is then broken into two.

What happens if you break a stick a second time?

(If we picked the shorter piece to break a second time, we could never get a triangle as the sum of the lengths of the two parts created by that break would be shorter than the third part.) We will assume that each of the two breakpoints is uniformly distributed along the piece of the stick being broken. Let be iid uniform (0,1) random variables.

What is the probability of making a triangle with an integral?

Now since is uniform (0,1), the probability inside the integral is simply the length of the interval which is . Notice that by breaking the stick in two steps rather than one (scenario 1) increases the chances that you will be able to make a triangle from 25\% to over 38.6\%. 8 clever moves when you have $1,000 in the bank.