AP EAMCET · Maths · Probability

If $x$ is chosen at random from the set $\{1, 2.3, 4\}$ and $y$ is chosen at random from the set $\{5, 6, 7\}$ , then the probability that xy will be even is

A $\frac{5}{6}$
B $\frac{1}{6}$
C $\frac{1}{2}$
D $\frac{2}{3}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{2}{3}$

Step-by-step Solution

Detailed explanation

Given, x is chosen at random from the set 1,2.3,4, And y is chosen at random from the set 5,6,7, Now given that xy will be even, then number of outcomes will be 1,6,2,5,2,6,2,7,3,6,4,5,4,6,4,7→8 outcomes Now total sample space will be 4×3=12, Now probability will…

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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If x is chosen at random from the set 1,2.3,4 and y is chosen at random from the set 5,6,7, then the probability that xy will be even is

Step-by-step Solution

If $x$ is chosen at random from the set $\{1, 2.3, 4\}$ and $y$ is chosen at random from the set $\{5, 6, 7\}$ , then the probability that xy will be even is