Question

square roots of prime numbers between 1-20​

Answer 1

Answer:

1

15

A random number between 1 and 20 is chosen. What is the probability that its square root will not be an integer?

Is there any app to track all my FDs, mutual funds, stocks, or any other such investments? I need a centralized place where I can check my assets.

Most of us have our money invested and divided across places such as savings accounts, fixed deposits, mutual funds, bonds, share

Siddharth Vishwanath

Answered August 3, 2014

Contrary to the answers given earlier - all of which were absolutely correct, of course - I'd like to address the case where you're sampling random numbers from the continuous Real line, as opposed to the discrete set of integers between 1 and 20.

In this case, the chosen random number (or the Random variable in the parlance of a statistician) assumes a continuous distribution with a uniform probability density function. X ~ Uniform[1,20]

The numbers of interest are 1,4,9 and 16. However, the Reimann sum of the areas of the rectangles corresponding to these numbers limit to zero. Hence, P[ x ∈ [1,20]\{1,4,9,16}] = 1 - P[x ∈ {1,4,9,16}] = 1.

So, there is an almost sure convergence that the random number chosen will not have an integer square root. I hope this helps. :)