A random variable X has the following probability distribution:
| \(X\) | 0 | 1 | 2 | 3 |
| \(P(X)\) | \(k\) | \(3k\) | \(4k\) | \(2k\) |
Then \(P(X \ge 2)\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.6
The probabilities of a distribution add up to 1:
\(k + 3k + 4k + 2k = 1\)
\(10k = 1\), so \(k = 0.1\)
The event \(X \ge 2\) means X = 2 or X = 3:
\(P(X \ge 2) = 4k + 2k = 6k\)
\(= 6 \times 0.1 = 0.6\)
Why the other options are incorrect
Option (1) 0.4 — Incorrect. This is \(k + 3k = 0.4\), the probability of \(X \le 1\).
Option (2) 0.2 — Incorrect. This is \(2k = 0.2\), the probability of X = 3 alone.
Option (4) 0.8 — Incorrect. This is \(1 - 2k = 0.8\), the probability of \(X \le 2\).