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.)
Transcript text: Homework: 7A Fundamentals of Probability
Question 4, 7.A.15
HW Score: 15.79\%, 3 of 19 points
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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.)
Solution
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
Identify the possible outcomes for each day: H or S.
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 \(\boxed{\{HH, HS, SH, SS\}}\).