Probability of Prime Numbers

Introduction :

The probability can be explained briefly as the “N” number of possible out comes of the event, in that “n” number of possible put comes is favor for X. Then the probability of X is the ratio of number out comes favor for the X to the total number of possible event. This is called as probability. In this article we see about the probability of  prime numbers.

Formula Used for the Probability:

Statement: Probability is nothing but the ratio of possible out come for selected event to the total number of out comes.

Formula – To find the probability as



Let us see the problem using the probability for prime numbers.

Example Problem - Probability of Prime Numbers:

Example Problem - Probability of Prime Numbers:

Example 1:

In class room there are 20 members, First ten members are selected as A team and next ten members are selected as B team. How many of the prime numbers in A team only.

Solution:

To find the prime number in first ten members only

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, in that 1, 2, 3, 5, 7 are the prime numbers.

Thus

The total number of possible out comes = 10
Selected event as prime number in A team = 5
Formula: p(A) = `(n(a))/(n(s))`

P(A) = `(5)/(10)` = `1/2`

Answer: The probability of prime number in A team is ½


Example 2:

In a box consists of numbers, In that bow we pick numbers as follow.

3, 4, 8, 56, 23, 89, 11, 43, 65, 67, 9, 10, 15, 24, 2, 14, 13, 7, 29, 81

Solution:

Step 1: Find the prime numbers from the picked number in box.

That is 3, 23, 11, 67, 2, 13, 7, 29

Thus

The total number of possible out comes = 20
Selected event as prime number in picked number from box = 8
Formula: p(A) = `(n(a))/(n(s))`

P(A) = `(8)/(20)` = `(2)/(5)`

Answer: The probability of prime number in in picked number from box is  `(2)/(5)`