Questions: A coin will be tossed twice, and each toss will be recorded as heads (H) or tails (T). Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the first toss is heads. Use the format H T to mean that the first toss is heads and the second is tails. If there is more than one element in the set, separate them with commas. Sample space: Event that the first toss is heads:

A coin will be tossed twice, and each toss will be recorded as heads (H) or tails (T).
Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the first toss is heads.

Use the format H T to mean that the first toss is heads and the second is tails. If there is more than one element in the set, separate them with commas.

Sample space:

Event that the first toss is heads:

Transcript text: A coin will be tossed twice, and each toss will be recorded as heads $(H)$ or tails ( $T$ ). Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the first toss is heads. Use the format $H T$ to mean that the first toss is heads and the second is tails. If there is more than one element in the set, separate them with commas. Sample space: $\square$ Event that the first toss is heads: $\square$

Solution

Solution Steps

Step 1: Construct the Sample Space

To construct the sample space, we enumerate all possible combinations of outcomes across the $N=2$ events. Given the outcomes per event as [['H', 'T'], ['H', 'T']], the sample space $S$ is constructed as follows: $$S = [('H', 'H'), ('H', 'T'), ('T', 'H'), ('T', 'T')]$$ This results in a total of 4 possible outcomes.

Step 2: Identify Outcomes for the Specified Event

The specified condition for filtering outcomes is: "outcome[0] == 'H'". Applying this condition, we filter the sample space to include only those outcomes that meet the condition. The outcomes that meet the specified condition are: $$[('H', 'H'), ('H', 'T')]$$ This results in 2 outcomes that satisfy the specified condition.

Final Answer:

The sample space for the sequence of independent events is [('H', 'H'), ('H', 'T'), ('T', 'H'), ('T', 'T')]. The outcomes that satisfy the specified condition "outcome[0] == 'H'" are [('H', 'H'), ('H', 'T')].

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