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Problem 1

# Describe the sample space $$S$$ of the experiment, and list the elements of the given event. (Assume that the coins are distinguishable and that what is observed are the faces or numbers that face up.) Two coins are tossed; the result is at most one tail.

Expert verified
The sample space $$S$$ of the experiment where two distinguishable coins are tossed is: $$S =$$ {HH, HT, TH, TT}. The elements of the event with at most one tail are: {HH, HT, TH}.
See the step by step solution

## Step 1: Identify the sample space of the overall experiment

Since there are two coins being tossed, and each coin has two possible outcomes - heads (H) and tails (T) - the overall sample space S can be found using the multiplication principle. With two possibilities from each coin, there are 2 x 2 = 4 possible outcomes. Let's label the coins as Coin 1 and Coin 2.

## Step 2: List all possible outcomes of the sample space S

Enumerate the 4 possible outcomes for the two distinguishable coins as follows: 1. Coin 1 shows a Head, and Coin 2 shows a Head (HH) 2. Coin 1 shows a Head, and Coin 2 shows a Tail (HT) 3. Coin 1 shows a Tail, and Coin 2 shows a Head (TH) 4. Coin 1 shows a Tail, and Coin 2 shows a Tail (TT) So, the sample space S = {HH, HT, TH, TT}.

## Step 3: Identify the elements of the event with at most one tail

According to the problem, the event we are interested in is at most one tail showing up when the coins are tossed. So, we need to find the outcomes from the sample space S where one or no tail is observed. From the possible outcomes listed in Step 2, we can see that outcomes 1 (HH), 2 (HT), and 3 (TH) meet the condition, while outcome 4 (TT) doesn't.

## Step 4: List the elements of the event

Based on the outcomes identified in Step 3, the elements of the event where there are at most one tail are: {HH, HT, TH}.

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