probability of primes.

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What is the probability that a prime number has its unit digit equal to 1 ?

Details and assumptions:

The number has more than 1 digit.
03 is not a 2-digit number.
As there are infinite primes,assume that the prime numbers' distribution is uniform.

\frac{1}{4}

\frac{1}{10}

\frac{1}{9}

\frac{1}{5}

1 solution

Vinay Sipani
Jun 22, 2014

As it is given that the prime number is of more than 1 digit, the numbers/digits possible at unit's place are 1,3,7,9 . All even digits and 5 are excluded as they are divisible by 2 and 5.

Hence the probability of occurence of 1 at unit's place is $\frac{1}{4}$ .

Note: You cannot select from a countably infinite set at random. There is no uniform distribution on the integers, or the prime numbers. As such, the question is not mathematically correct.

Calvin Lin Staff - 6 years, 11 months ago

I have run a program to test it, and in the primes smaller than 100000, there are 9592 primes, in which 2387 ends with 1. In the primes smaller than 1000000, there are 78498 primes, in which 19617 ends with 1.

2387/9592=0.248853211

19617/78498=0.24990445616

Kenny Lau - 6 years, 11 months ago

You mean it is not proven whether the distribution of primes is uniform or not.

Alright,meanwhile I will edit the question.

Vinay Sipani - 6 years, 11 months ago

This was a really weird question....(no offense). It's just that I selected the most non-probable answer I felt and that turned out to be correct....

Tanya Gupta - 6 years, 11 months ago

Thank you...Will take it as a compliment..

Vinay Sipani - 6 years, 11 months ago

probability of primes.

Details and assumptions:

1 solution

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