isi-entrance 2024 Q14

isi-entrance · India · UGA Discrete Probability Distributions Limit and Convergence of Probabilistic Quantities

In a room with $n \geqslant 2$ people, each pair shakes hands between themselves with probability $\frac{2}{n^2}$ and independently of other pairs. If $p_n$ is the probability that the total number of handshakes is at most 1, then $\lim_{n \rightarrow \infty} p_n$ is equal to
(A) 0
(B) 1
(C) $e^{-1}$
(D) $2e^{-1}$

In a room with $n \geqslant 2$ people, each pair shakes hands between themselves with probability $\frac{2}{n^2}$ and independently of other pairs. If $p_n$ is the probability that the total number of handshakes is at most 1, then $\lim_{n \rightarrow \infty} p_n$ is equal to\\
(A) 0\\
(B) 1\\
(C) $e^{-1}$\\
(D) $2e^{-1}$

Paper Questions

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