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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. The set of outcomes when a coin is tossed twice and then a die is rolled. Write the set in terms of A and/or B. OBXAXA OAXBXB OAX AX B OBXBXA List the elements of the set. O {(HH), (HT), (TH), (TT), (1, 2, 3, 4, 5, 6)} O {(H1), (H2), (H3), (H4), (H5), (H6), (T1), (T2), (73), (T4), (T5), (T6)} O {(H, T), (1, 2, 3, 4, 5, 6)} O {HH1, HH2, HH3, HH4, HH5, HH6, HT1, HT2, HT3, HT4, HT5, HT6, TH1, TH2, TH3, TH4, TH5, TH6, TT1, TT2, TT3, TT4, TT5, TT6}

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. The set of outcomes when a coin is tossed twice and then a die is rolled. Write the set in terms of A and/or B. OBXAXA OAXBXB OAX AX B OBXBXA List the elements of the set. O {(HH), (HT), (TH), (TT), (1, 2, 3, 4, 5, 6)} O {(H1), (H2), (H3), (H4), (H5), (H6), (T1), (T2), (73), (T4), (T5), (T6)} O {(H, T), (1, 2, 3, 4, 5, 6)} O {HH1, HH2, HH3, HH4, HH5, HH6, HT1, HT2, HT3, HT4, HT5, HT6, TH1, TH2, TH3, TH4, TH5, TH6, TT1, TT2, TT3, TT4, TT5, TT6}

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.

The set of outcomes when a coin is tossed twice and then a die is rolled.

Write the set in terms of A and/or B.

B × A × A
A × B × B    A × A × B
B × B × A


List the elements of the set.

{(HH), (HT), (TH), (TT), (1, 2, 3, 4, 5, 6)}
{(H1), (H2), (H3), (H4), (H5), (H6), (T1), (T2), (T3), (T4), (T5), (T6)} 
   {(H, T), (1, 2, 3, 4, 5, 6)}{HH1, HH2, HH3, HH4, HH5, HH6, HT1, HT2, HT3, HT4, HT5, HT6, TH1, TH2, TH3, TH4, TH5, TH6, TT1, TT2, TT3, TT4, TT5, TT6}
 
ATTACHED IS THE IMAGE TO QUESTION
**Title: Probability and Set Theory: Coin Toss and Die Roll** **Introduction** In this exercise, we explore the combinations of outcomes when a coin is tossed twice and a die is rolled. These concepts are essential in understanding probability and set theory. **Definitions** - Let \( A = \{H, T\} \) be the set of outcomes when a coin is tossed. - Let \( B = \{1, 2, 3, 4, 5, 6\} \) be the set of outcomes when a die is rolled. **Problem Statement** Determine the set of outcomes when a coin is tossed twice, followed by a die roll. **Question 1: Write the set in terms of A and/or B.** Options: - \( B \times A \times A \) - \( A \times B \times B \) - \( A \times A \times B \) (Correct Answer) - \( B \times B \times A \) **Question 2: List the elements of the set.** Options: - \(\{(HH), (HT), (TH), (TT), (1, 2, 3, 4, 5, 6)\}\) - \(\{(H1), (H2), (H3), (H4), (H5), (H6), (T1), (T2), (T3), (T4), (T5), (T6)\}\) (Correct Answer) - \(\{(H, T), (1, 2, 3, 4, 5, 6)\}\) - \(\{HH1, HH2, HH3, HH4, HH5, HH6, HT1, HT2, HT3, HT4, HT5, HT6, TH1, TH2, TH3, TH4, TH5, TH6, TT1, TT2, TT3, TT4, TT5, TT6\}\) **Conclusion** The correct representation of the set is \( A \times A \times B \), listing all possible outcomes when tossing a coin twice and rolling a die. Understanding these combinations helps build foundational knowledge in probability and combinatorics.
Transcribed Image Text:**Title: Probability and Set Theory: Coin Toss and Die Roll** **Introduction** In this exercise, we explore the combinations of outcomes when a coin is tossed twice and a die is rolled. These concepts are essential in understanding probability and set theory. **Definitions** - Let \( A = \{H, T\} \) be the set of outcomes when a coin is tossed. - Let \( B = \{1, 2, 3, 4, 5, 6\} \) be the set of outcomes when a die is rolled. **Problem Statement** Determine the set of outcomes when a coin is tossed twice, followed by a die roll. **Question 1: Write the set in terms of A and/or B.** Options: - \( B \times A \times A \) - \( A \times B \times B \) - \( A \times A \times B \) (Correct Answer) - \( B \times B \times A \) **Question 2: List the elements of the set.** Options: - \(\{(HH), (HT), (TH), (TT), (1, 2, 3, 4, 5, 6)\}\) - \(\{(H1), (H2), (H3), (H4), (H5), (H6), (T1), (T2), (T3), (T4), (T5), (T6)\}\) (Correct Answer) - \(\{(H, T), (1, 2, 3, 4, 5, 6)\}\) - \(\{HH1, HH2, HH3, HH4, HH5, HH6, HT1, HT2, HT3, HT4, HT5, HT6, TH1, TH2, TH3, TH4, TH5, TH6, TT1, TT2, TT3, TT4, TT5, TT6\}\) **Conclusion** The correct representation of the set is \( A \times A \times B \), listing all possible outcomes when tossing a coin twice and rolling a die. Understanding these combinations helps build foundational knowledge in probability and combinatorics.
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