Out of 40 consecutive natural numbers,two are | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) In a set of $40$ consecutive natural numbers,there are exactly $20$ odd numbers and $20$ even numbers.For the sum of two chosen numbers to be odd,

Vedclass · Accepted Answer

$\frac{20}{39}$

Vedclass · Answer

(B) In a set of $40$ consecutive natural numbers,there are exactly $20$ odd numbers and $20$ even numbers.For the sum of two chosen numbers to be odd,one number must be odd and the other must be even.The total number of ways to choose $2$ numbers out of $40$ is given by ${}^{40}C_2 = \frac{40 	imes 39}{2} = 780$.The number of ways to choose one odd number and one even number is ${}^{20}C_1 	imes {}^{20}C_1 = 20 	imes 20 = 400$.Therefore,the required probability is $P = \frac{400}{780} = \frac{40}{78} = \frac{20}{39}$.

Out of $40$ consecutive natural numbers,two are chosen at random. The probability that the sum of the numbers is odd is:

Similar Questions

When two dice are thrown,what is the probability that the sum of the numbers appearing on them is an even number?

Two dice are thrown. Find the probability of getting an even number as the sum.

$A$ man draws a card from a pack of $52$ playing cards,replaces it,and shuffles the pack. He continues this process until he gets a card of spade. The probability that he will fail the first two times is

$A$ dice is rolled three times. The probability of getting a larger number than the previous number each time is:

$2$ dice are thrown. Find the probability of getting a doublet of even numbers.

Vedclass Test Series

Exam Paper Generator

Online Exam Module