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Chapter 7: Problem 2

List the simple events associated with each experiment. A card is selected at random from a standard 52 -card deck, and its suit- hearts \((h)\), diamonds \((d)\), spades \((s)\), or clubs (c) - is recorded.

Short Answer

Expert verified
The simple events associated with the experiment of selecting a card at random from a 52-card deck and recording its suit are: \(h\), \(d\), \(s\), and \(c\).

Step by step solution

01

Identify the possible suits

In a standard 52-card deck, there are four suits: hearts (h), diamonds (d), spades (s), and clubs (c).
02

Define the simple events

A simple event consists of selecting a card with a specific suit. Since there are four possible suits, we have four simple events, one for each suit: 1. Selecting a heart (h) 2. Selecting a diamond (d) 3. Selecting a spade (s) 4. Selecting a club (c)
03

List the simple events

The simple events associated with the experiment of selecting a card at random from a 52-card deck and recording its suit are: 1. h 2. d 3. s 4. c

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simple Events
In probability, **simple events** are the most basic possible outcomes of a random experiment. They cannot be broken down into smaller outcomes. In the context of drawing a card from a standard 52-card deck, a simple event is the result of drawing a card with a specific suit. This means that each card draw that results in either a heart, diamond, spade, or club represents a simple event. Simple events are critical as they serve as the building blocks of probability calculations, allowing us to understand the likelihood of various outcomes in more complex scenarios.
Random Experiments
**Random experiments** are processes or actions that result in one uncertain outcome from several possible ones. They are fundamental in probability theory because they help in understanding and modeling uncertainty. Selecting a card from a deck is a classic example of a random experiment. The outcome, which suit the card belongs to, cannot be predicted with certainty prior to the draw; hence, it is random. This randomness is a key feature because it ensures each card has an equal chance of being selected, making the entire process unbiased and fair.
52-card Deck
A standard **52-card deck** is a collection of playing cards used in countries around the world. It is made up of four suits, each containing 13 cards. These suits are hearts, diamonds, spades, and clubs. Knowing the composition of a 52-card deck is essential in solving problems related to probability, especially in exercises that involve finding the likelihood of drawing cards of specific suits or ranks. By understanding the deck's structure, it becomes easier to calculate probabilities, like the chance of drawing a card of a particular suit.
Suit of Cards
**Suits of cards** are categories that divide a deck into four distinct types: hearts, diamonds, spades, and clubs. Each suit consists of 13 cards, ranging from ace through king. Understanding suits is crucial when performing probabilistic exercises since they determine the simple events we list when carrying out experiments like card draws. Each suit holds equal weight in a deck, meaning each has a 1 in 4 chance of being drawn in a single random selection. Knowing these categories enables us to effectively model and predict outcomes and calculate probabilities in card-related problems.

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