Math Problem Statement
If you flip two coins, what are the possible outcomes? Figure out the outcomes and write out the sample spaces. Start with Coin 1, then Coin 2.
Solution
This is a classic probability problem. The goal is to determine all possible outcomes when flipping two coins, considering both coins' heads (h) and tails (t).
The sample space can be filled out systematically:
- Coin 1 lands heads (h), Coin 2 lands heads (h): hh.
- Coin 1 lands heads (h), Coin 2 lands tails (t): ht.
- Coin 1 lands tails (t), Coin 2 lands heads (h): th.
- Coin 1 lands tails (t), Coin 2 lands tails (t): tt.
Completed Grid:
| Coin 2 \ Coin 1 | Heads (h) | Tails (t) |
|---|---|---|
| Heads (h) | hh | ht |
| Tails (t) | th | tt |
This table now represents the full set of sample spaces for flipping two coins.
Would you like additional explanation on how probabilities for each outcome are calculated?
5 Related Questions:
- What is the total probability of all outcomes in the sample space?
- How can we calculate the probability of getting at least one head?
- How does the sample space change if a third coin is added?
- What is the probability of flipping two tails in a row?
- How are these probabilities affected by a biased coin?
Tip:
When working with probability, always double-check that the total number of outcomes in your sample space matches all possible combinations. This ensures accuracy!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability
Sample Space
Formulas
Counting principle for independent events: Total outcomes = m × n
Theorems
Basic Probability Principles
Suitable Grade Level
Grades 6-8