Question

Let $A=\{H, T\}$ be the set of outcomes when a coin is tossed, and let $B=\{1,2,3,4,5,6\}$ be the set of outcomes when a die is rolled. Write each set in terms of A and/or $B$ and list its elements. The set of outcomes when a coin is tossed twice and then a die is rolled.

Name: Problem 46, Chapter 6: Finite Mathematics and Applied Calculus
Uploaded: 2023-08-24T20:36:39-08:00
Duration: 53 s
Channel: William Mead
Description: Let A={H, T} be the set of outcomes when a coin is tossed, and let B={1,2,3,4,5,6} be the set of outcomes when a die is rolled. Write each set in terms of A and/or B and list its elements. The set of outcomes when a coin is tossed twice and then a die is rolled.

   Let $A=\{H, T\}$ be the set of outcomes when a coin is tossed, and let $B=\{1,2,3,4,5,6\}$ be the set of outcomes when a die is rolled. Write each set in terms of A and/or $B$ and list its elements.  
The set of outcomes when a coin is tossed twice and then a die is rolled.

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 5th Edition

Chapter 6, Problem 46

Instant Answer

Solved by Expert William Mead

08/24/2023

Step 1

The possible outcomes for this are: HH, HT, TH, TT. We can represent this set as $A \times A = \{(H,H), (H,T), (T,H), (T,T)\}$. Show more…

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Let $A=\{H, T\}$ be the set of outcomes when a coin is tossed, and let $B=\{1,2,3,4,5,6\}$ be the set of outcomes when a die is rolled. Write each set in terms of A and/or $B$ and list its elements. The set of outcomes when a coin is tossed twice and then a die is rolled.

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Key Concepts

Cartesian Product

The Cartesian product is an operation that returns a set from multiple sets, consisting of all ordered pairs (or tuples) where the first element is from the first set and the second element is from the second set. In the case of tossing a coin twice, it involves taking the Cartesian product of the set {H, T} with itself.

Set Notation

Set notation provides a formal means of describing collections of objects, such as outcomes in an experiment. It allows for defining experiments like tossing a coin twice using mathematical expressions, such as {H, T} × {H, T}, which represents all possible ordered outcomes.

Sample Space

A sample space is the set of all possible outcomes of a probability experiment. In this context, it means the complete list of outcomes when a coin is tossed twice, ensuring that no possible outcome is omitted.

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