There are 6 cards numbered 1 to 6, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two cards drawn. Then \(P(X \gt 3)\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{14}{15}\)
Two different cards are drawn, so the number of equally likely pairs is
\({}^{6}C_{2} = 15\)
The smallest possible sum is 1 + 2 = 3, and only the pair {1, 2} gives it. So X > 3 fails only for that pair. Using the complement:
\( \displaystyle P(X \gt 3) = 1 - P(X = 3) = 1 - \frac{1}{15} = \frac{14}{15} \)