Question

Question: What is the probability that a randomly selected integer chosen from the first 100 positive integers is odd?

Short answer

Answer

12 chances are there for getting first 100 positive integer odd.

Step-by-step solution

Given

The probability that a randomly selected integer chosen from the first$100$positive integers is odd is $P\left(E\right)=12$

Explanation

As per the problem an integer is randomly chosen from first $100$ positive integers.

If S represents the sample space and E represents the event. Then the probability of occurrence of favourable event is given by the formula as given below:

$P\left(E\right)=n\left(E\right)n\left(S\right)$

Calculation  

Here we are choosing from the first $100$ positive integers so we have $n\left(S\right)=100$

The number of odd integers in the first $100$ positive integers are as follows

$\{1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31$ }

So, we have $n\left(E\right)=50$

Now substitute the values in the above formula we get

$P\left(E\right)=50100\Rightarrow P\left(E\right)=12$