A coin will be tossed three times, 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 *HTH* to mean that the first toss is heads, the second is tails, and the third is heads. If there is more than one element in the set, separate them with commas.

The **sample space** for tossing a coin three times contains all possible combinations of heads (*H*) and tails (*T*). These combinations are the outcomes of the three tosses. The sample space is:

\[ S = \{ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT \} \]

Now, for the event that the **first toss is heads**, we only consider the outcomes where the first toss is *H*. The outcomes for this event are:

\[ \{ HHH, HHT, HTH, HTT \} \]

Would you like further details on any step, or do you have any questions?

Here are 5 related questions to explore further:
1. What is the probability of getting exactly two heads in three tosses?
2. What is the probability of getting at least one head in three tosses?
3. How many outcomes result in no heads?
4. What is the probability of getting tails on all three tosses?
5. What is the probability of getting heads on the second toss?

**Tip:** In probability, the total number of outcomes in the sample space is crucial for calculating the likelihood of events. Make sure to count all possible outcomes carefully!

A coin will be tossed three times, 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 HTH to mean that the first toss is heads, the second is tails, and the third is heads. If there is more than one element in the set, separate them with commas.

Discover the complete sample space for three coin tosses and learn how to find the outcomes where the first toss is heads. This probability problem covers key concepts such as sample space, events, and outcome analysis. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation