Two numbers are selected at random from 40 co | vedclass

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Question

(B) In $40$ consecutive natural numbers,there are $20$ odd numbers and $20$ even numbers.For the sum of two numbers to be odd,one number must be even

Vedclass · Accepted Answer

$20/39$

Vedclass · Answer

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

Two numbers are selected at random from $40$ consecutive natural numbers. What is the probability that the sum of the numbers is odd?

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