Question

There are 25 prime numbers between 1 and 100. There are 46 prime numbers between 1 and 200. Which situation is more likely? Explain your reasoning. 1. A computer produces a random number between 1 and 100 that is prime. 2. A computer produces a random number between 1 and 200 that is prime.

Answer 1

One.

Explanation:

There is a 25% chance of situation one happening.

`(prime)/(total) =(25)/(100) = 0.25=25`%

There is a 23% chance of situation two happening.

`(prime)/(total) =(46)/(200)=0.23=23`%

Since the chance is two percent bigger from situation one, situation one should be the one that is more likely to happen.