Two cards are randomly selected from an ordinary playing deck. What is the probability that they

step 1 Hello students in problem 18 of chapter 2nd we have asked that two cards are randomly selected f

Two cards are randomly selected from an ordinary playing...

Key Concepts

Probability

Probability is the branch of mathematics that deals with quantifying the likelihood of events occurring. In problems like this, it is often calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes in the sample space.

Combinatorics

Combinatorics involves counting and arranging objects in specific configurations. In the context of card problems, combinatorial methods such as combinations are used to determine how many different pairs of cards can be drawn from a deck without regard to order.

Sampling Without Replacement

Sampling without replacement means that once a card is drawn from the deck, it is not returned before the next draw. This concept is crucial because it affects the probabilities of successive events, as the total number of available cards decreases with each draw.

Deck Composition

Understanding the composition of a standard playing deck is fundamental in card probability problems. A standard deck typically has 52 cards, with specific numbers designated for face cards, aces, and numbered cards, each contributing differently towards achieving certain combinations like a blackjack.

Event Definition

Defining the event precisely is key in probability. In this context, identifying what constitutes a 'blackjack' (a specific combination of cards) is essential for determining which outcomes should be considered favorable in the calculation.

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