GATE CS 2011 Q.34 (CS Q.34): Probability and Statistics

A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card?

$1/5$

$4/25$

$1/4$

$2/5$

Official answer and solution

Official answer: A
From: Official GATE 2011 answer key

Solution

Calculate the ratio of favorable ordered outcomes to total ordered pairs without replacement.

Two cards are drawn without replacement from a deck of 5 cards $\{1, 2, 3, 4, 5\}$ . The total number of ordered pairs $(c_1, c_2)$ is:

N = 5 \times 4 = 20

We require the first card to be one higher than the second card ( $c_1 = c_2 + 1$ ). The favorable pairs are:

\{(2, 1), (3, 2), (4, 3), (5, 4)\}

There are exactly 4 favorable outcomes. The required probability is:

P = \frac{4}{20} = \frac{1}{5}

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2011 Computer Science and Information Technology (CS)
Question: 34 of 65, printed as CS Q.34
Section: Computer Science and Information Technology

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