TS EAMCET · Maths · Probability

Out of $40$ consecutive integers two integers are drawn at random. The probability that their sum is odd is

A $\frac{15}{29}$
B $\frac{20}{39}$
C $\frac{25}{29}$
D $\frac{40}{39}$

Verified Solution

Answer & Solution

Correct Answer

(B) $\frac{20}{39}$

Step-by-step Solution

Detailed explanation

To find probability of selecting two numbers out of 40 integers Total number of elements in sample-space=Number of ways of drawing two number out of 40 numbers=C240 Crn= n! r! n-r! = 40!2! (40-2!) =40!2(38!) =20×39 If we are drawing…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Out of 40 consecutive integers two integers are drawn at random. The probability that their sum is odd is

Step-by-step Solution

Out of $40$ consecutive integers two integers are drawn at random. The probability that their sum is odd is