Questions: Consider the following. (Assume that the coins are distinguishable and that what is observed are the faces or numbers that face up.) Three coins are tossed; the result is at most one tail. Which of the following sets of elements are included in the sample space? (Select all that apply.) TTH HIT HHT HTH HHH THH TIT THT

Solution Steps

To solve this problem, we need to determine the possible outcomes when three coins are tossed, with the condition that the result is at most one tail. This means we can have zero or one tail in the outcome. We will list all possible outcomes with zero or one tail and check which of the given options match these outcomes.

When tossing three distinguishable coins, the outcomes can be represented as combinations of heads (H) and tails (T). Given the condition of at most one tail, the possible outcomes are:

• \( HHH \)
• \( HHT \)
• \( HTH \)
• \( THH \)

We need to check which of the provided options are included in the identified possible outcomes. The options given are:

• \( TTH \)
• \( HIT \)
• \( HHT \)
• \( HTH \)
• \( HHH \)
• \( THH \)
• \( TIT \)
• \( THT \)

From the evaluation, the options that match the possible outcomes are:

• \( HHT \)
• \( HTH \)
• \( HHH \)
• \( THH \)

Final Answer