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Found in: Page 451

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

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

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

See the step by step solution

Step 1: Given

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

Step 2: 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:

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

Step 3: 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

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

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

Now substitute the values in the above formula we get

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