Question

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 > 3) is:

• A. $\frac{14}{15}$
• B. $\frac{1}{15}$
• C. $\frac{11}{12}$
• D. $\frac{1}{12}$

Answer 1

Answer: (A)

$\frac{14}{15}$

Answer 2

The total number of ways to choose 2 cards from 6 is:
$\binom{6}{2} = 15.$
The event $X > 3$ means the sum of the numbers on the two cards is greater than 3. The only pair with a sum $\leq 3$ is $(1, 2)$, which occurs in 1 way.

Thus, the number of favorable outcomes for $X > 3$ is:
$15 - 1 = 14.$

The probability is:
$P(X > 3) = \frac{14}{15}.$