Questions: Suppose we describe the weather as either hot (H) or stormy (S). Answer parts (a) and (b) below. a. Using the letters H and S, list all the possible outcomes for the weather on two consecutive days. (Use a comma to separate answers as needed.)

Suppose we describe the weather as either hot (H) or stormy (S). Answer parts (a) and (b) below.
a. Using the letters H and S, list all the possible outcomes for the weather on two consecutive days.
(Use a comma to separate answers as needed.)
Transcript text: Homework: 7A Fundamentals of Probability Question 4, 7.A.15 HW Score: 15.79\%, 3 of 19 points Part 1 of 2 Points: 0 of 1 Question list Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Suppose we describe the weather as either hot $(\mathrm{H})$ or stormy (S). Answer parts (a) and (b) below. a. Using the letters H and S , list all the possible outcomes for the weather on two consecutive days. $\square$ (Use a comma to separate answers as needed.)
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Solution

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Solution Steps

To solve this problem, we need to list all possible outcomes for the weather on two consecutive days, where each day can either be hot (H) or stormy (S). We can use a combination of these two letters to represent each possible outcome.

Solution Approach
  1. Identify the possible outcomes for each day: H or S.
  2. Generate all combinations of these outcomes over two days.
Step 1: Identify Possible Outcomes

We define the weather for each day as either hot (\(H\)) or stormy (\(S\)). For two consecutive days, we can represent the outcomes as combinations of these two states.

Step 2: Generate Combinations

The possible outcomes for the weather over two consecutive days can be represented as follows:

  • Day 1: \(H\), Day 2: \(H\) → Outcome: \(HH\)
  • Day 1: \(H\), Day 2: \(S\) → Outcome: \(HS\)
  • Day 1: \(S\), Day 2: \(H\) → Outcome: \(SH\)
  • Day 1: \(S\), Day 2: \(S\) → Outcome: \(SS\)

Thus, the complete list of possible outcomes is: \[ \{HH, HS, SH, SS\} \]

Final Answer

The possible outcomes for the weather on two consecutive days are \(\boxed{\{HH, HS, SH, SS\}}\).

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