JEE Main 2022 · 29 Jun · Shift 2 · Mathematics Q16

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MathematicsSingle correct+4 / -1Question 16 of 90

The probability that a relation R from $\{x,y\}$ to $\{x,y\}$ is both symmetric and transitive, is equal to

\dfrac5{16}

\dfrac9{16}

\dfrac{11}{16}

\dfrac{13}{16}

Answer and worked solution

Official answer: A

Symmetric relations on $\{x,y\}$ : $2^3=8$ . Those containing the pair $(x,y),(y,x)$ are transitive only with both loops: 1. Without the pair: all 4 are transitive.

Probability $\frac5{16}$ .

(A)

Topics:Relations Classical probability

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JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 16