Two numbers are selected at random (without replacement) from the first three positive integers. Let X denote the larger of the two integers, then the probability distribution of X is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → P(X = 2) = 1/3, P(X = 3) = 2/3
From {1, 2, 3}, two numbers can be chosen in \({}^{3}C_{2} = 3\) equally likely ways. The larger number in each pair:
\(\{1, 2\} \rightarrow 2\)
\(\{1, 3\} \rightarrow 3\)
\(\{2, 3\} \rightarrow 3\)
So X = 2 in one case out of three and X = 3 in two cases:
\( \displaystyle P(X = 2) = \frac{1}{3}, \quad P(X = 3) = \frac{2}{3} \)