A number is chosen at random among the first 100 natural numbers. Find the probability that the number chosen is prime.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The probability of obtaining a Prime Number among the first 100 natural numbers is 1/4. The possibility of an event happening or not happening is known as probability. The probability is calculated between 0 and 1, where 0 is the impossibility of an event happening whereas 1 is the possibility of an event happening.

Table of content

1. Probability of Getting Prime Number Among First 100 Natural Numbers
2. A number is chosen at random among the first 100 natural numbers. Find the probability that the number chosen is prime.

Probability of Getting Prime Number Among First 100 Natural Numbers

If a number is chosen at random among the first 100 natural numbers, the possibility of it being a prime number can be calculated using the below-mentioned formula.

P(E) = Total number of outcomes/Number of favorable outcomes

Here, P(E) refers to the probability of an event.

In this case, the total number of outcomes = 100

Now, to find out the total number of favorable outcomes we will have to find out how many prime numbers are there.

The prime numbers among the first 100 natural numbers are –

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89, and 97.

Thus, the number of favorable outcomes = 25

Using the formula, the probability of the event = 100/25 = 1/4

Thus, among the first 100 natural numbers, the probability of getting a prime number is 1/4.

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