Question

A number is chosen at random from 2 to 16 inclusive. What is the probability that the number is prime?​

Answer 1

Answer:  2/5

==========================================================

Explanation:

A = list of primes between 2 and 16, inclusive for both endpoints

A = {2,3,5,7,11,13}

B = list of integers between 2 and 16, inclusive for both endpoints

B = {2,3,4,...,14,15,16}

The dots indicate the pattern continues, which means we don't have to write out every value.

There are n(A) = 6 items in set A and n(B) = 16-2+1 = 15 items in set B. I'm using the formula that a set like {p,p+1,p+2,...,q-2,q-1,q} has q-p+1 elements in it. This only works for integers and they must be consecutive. Also q > p.

Once we know how many items are in each set, we divide the two counts

P(finding a prime between 2 and 16) = n(A)/n(B) = 6/15 = 2/5