We will find that you must randomly pick n + 2 numbers to be sure of getting at least one that is odd.
So n is a positive integer, then the possible values of n are:
{1, 2, 3, 4, ...}
Let's take n = 1
Now, how many integers from 0 through 2n = 2*1 = 2 must you pick (randomly) in order to be sure of getting at least one that is odd?
So from 0 to 2 there are 3 numbers:
0, 1, 2
If you pick these randomly, the only way to be sure of getting an odd number is if you pick all 3 numbers.
If n = 2 we have that from 0 to 2*n there are:
0, 1, 2, 3, 4
5 options.
3 of which are even, then if you want to pick at least one odd number for sure, you must pick 4 numbers
if n = 3, from 0 to 2*n we have:
0, 1, 2, 3, 4, 5, 6
4 of these are even, so to be sure of getting an odd number, you must pick 5 of these numbers.
Notice that the number of even numbers is always n + 1, so for a random integer n, from 0 to 2n we will have n + 1 even numbers, so if we want to be sure of randomly selecting an odd number we need to pick n + 2 numbers.
If you want to learn more about random selections, you can read:
https://brainly.com/question/10678373
