Consider a 25×25 grid of city streets. Let S be the points of intersection of the streets, and let P be the set of paths from the bottom left corner to the top right corner of which consist of only walking to the right and up. A point s is chosen uniformly at random from S and then a path p is chosen uniformly at random from P. Over all (s,p) pairs, the probability that the point s is contained in the path p can be expressed as a/b where a and b are coprime positive integers. What is the value of a+b?
please answer its urgent
Give me a link to this problem?
it is of brilliant named site
GIVE A LINK TO THE PROBLEM?
AND SHOULD NOT YOU SOLVE IT ON YOUR OWN?
to ok. if you want to answer this on the site brilliant, you can by making an account but unfortunately, in every account, they have different sets of question basing on the level what you are in. this is such a very easy question.
but I found that you can share links once you solve the problem.
Can I have your link, please?
I think 49/625
Arnav thuje koi answer nahi bataye ga mat try kar
To solve this problem, we need to consider the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. In a 25x25 grid, there are (25+1) horizontal streets and (25+1) vertical streets, giving us a total of (26+26) = 52 streets. The number of intersections or points of S would then be (26)*(26) = 676.
Now, let's calculate the number of favorable outcomes, i.e., the number of paths that contain the chosen point s. To reach the top right corner from the bottom left corner, we need to take 25 steps to the right and 25 steps up. This can be thought of as a combination problem, where we need to choose 25 out of the total 50 steps to be taken as "up" steps. The number of such combinations is given by the binomial coefficient, often denoted as "n choose k" and calculated as C(n, k) = n! / (k!(n-k)!). In our case, we have C(50, 25) = 50! / (25! * (50-25)!) = (50! / 25!)^2.
Therefore, the number of favorable outcomes is (50! / 25!)^2.
To find the probability, we divide the number of favorable outcomes by the total number of outcomes:
Probability = (number of favorable outcomes) / (total number of outcomes)
= (50! / 25!)^2 / 676
Finally, we express the probability as a fraction a/b, where a is the numerator and b is the denominator.
Now, we can calculate the value of a+b by finding the sum of a and b.
(Note: The calculation of (50! / 25!)^2 can be computationally intensive, so it might not be feasible to calculate the exact numerical value.)