Question

What is the probability that the 2 and 3 of clubs are next to each other in a shuffled deck? Hint: Imagine the two cards accidentally stuck together and shuffled as one card.

Short answer

Answer

The probability that the 2 and 3 of clubs are next to each other in a shuffled deck is $\frac{1}{26}$

Step-by-step solution

Given Information

A deck of 52 cards is given.

Definition of Independent Event

When the order of arrangement is definite, the permutation is applied and when the order is not definite,combination is applied.

Finding the probability that the 2 and 3 of clubs are next to each other in a shuffled deck

Let the 2 and 3 of club stick together and is assumed to become a single card, this implies that the deck will have 51 cards. And the cards can be arranged inand the stuck cards can be arranged in.

The total arrangements possible is.

This implies that the number of outcomes favourable areand total number of outcomes are.

Apply the formula for probability, that isto get the probability that the 2 and 3 of clubs are next to each other in a shuffled deck.

Thus the required probability is.