Math Problem Statement
List the elements of the sample space for the experiment. A coin is flipped three times.
{HHH, HTH, HHT, HTT, THH, THT, TTH, TTT}
{HHH, TTT}
{HHH, HTH, HHT, HTT}, {THH, THT, TTH, TTT}
{HT, HT, HT}
{HHH}, {HTH}, {HHT}, {HTT}, {THH}, {THT}, {TTH}, {TTT}
{H, T}
Solution
The correct sample space for the experiment of flipping a coin three times includes all possible outcomes of those flips. The sample space is:
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
This includes all combinations of heads (H) and tails (T) for three flips.
The other options do not represent the complete sample space.
Would you like more details or have any questions? Here are some related questions for further exploration:
- What is the probability of getting exactly two heads in three flips?
- How many total outcomes are there when flipping a coin four times?
- What would be the sample space if a coin is flipped five times?
- Can you explain how to calculate the probabilities of specific outcomes in this sample space?
- How would the sample space change if the coin were biased?
Tip: Always ensure to consider all possible combinations when defining a sample space in probability experiments.
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Math Problem Analysis
Mathematical Concepts
Probability
Combinatorics
Formulas
Sample space = total outcomes for n trials
Theorems
Counting Principle
Suitable Grade Level
Grades 5-7