Using a sample-space diagram to calculate probability
Using a sample-space diagram to calculate probability.
- Identify the outcomes that are still possible after applying the condition.
- Use the number or probability meeting both requirements in the numerator.
- The denominator comes from the restricted sample space, not automatically the original total.
Example 1
Two independent fair spinners have numbers 1 to 2 and 1 to 2. Find the probability that their sum is at least 3.
| A \ B | 1 | 2 |
|---|---|---|
| 1 | 2 | 3 |
| 2 | 3 | 4 |
Black: given data. Blue: working we add.
Example 2
Two independent fair spinners have numbers 1 to 3 and 1 to 2. Find the probability that their sum is at least 4.
| A \ B | 1 | 2 |
|---|---|---|
| 1 | 2 | 3 |
| 2 | 3 | 4 |
| 3 | 4 | 5 |
Black: given data. Blue: working we add.
Your turn
Two independent fair spinners have numbers 1 to 4 and 1 to 2. Find the probability that their sum is at least 5.
| A \ B | 1 | 2 |
|---|---|---|
| 1 | 2 | 3 |
| 2 | 3 | 4 |
| 3 | 4 | 5 |
| 4 | 5 | 6 |
Black: given data. Blue: working we add.
Check answer
Two independent fair spinners have numbers 1 to 5 and 1 to 2. Find the probability that their sum is at least 6.
| A \ B | 1 | 2 |
|---|---|---|
| 1 | 2 | 3 |
| 2 | 3 | 4 |
| 3 | 4 | 5 |
| 4 | 5 | 6 |
| 5 | 6 | 7 |
Black: given data. Blue: working we add.
Check answer
Two independent fair spinners have numbers 1 to 2 and 1 to 3. Find the probability that their sum is at least 4.
| A \ B | 1 | 2 | 3 |
|---|---|---|---|
| 1 | 2 | 3 | 4 |
| 2 | 3 | 4 | 5 |
Black: given data. Blue: working we add.
Check answer
Two independent fair spinners have numbers 1 to 3 and 1 to 3. Find the probability that their sum is at least 4.
| A \ B | 1 | 2 | 3 |
|---|---|---|---|
| 1 | 2 | 3 | 4 |
| 2 | 3 | 4 | 5 |
| 3 | 4 | 5 | 6 |
Black: given data. Blue: working we add.
Check answer
Two independent fair spinners have numbers 1 to 4 and 1 to 3. Find the probability that their sum is at least 5.
| A \ B | 1 | 2 | 3 |
|---|---|---|---|
| 1 | 2 | 3 | 4 |
| 2 | 3 | 4 | 5 |
| 3 | 4 | 5 | 6 |
| 4 | 5 | 6 | 7 |
Black: given data. Blue: working we add.
Check answer
Two independent fair spinners have numbers 1 to 4 and 1 to 2. Find the probability that their sum is at least 5.
| A \ B | 1 | 2 |
|---|---|---|
| 1 | 2 | 3 |
| 2 | 3 | 4 |
| 3 | 4 | 5 |
| 4 | 5 | 6 |
Black: given data. Blue: working we add.
Two independent fair spinners have numbers 1 to 5 and 1 to 2. Find the probability that their sum is at least 6.
| A \ B | 1 | 2 |
|---|---|---|
| 1 | 2 | 3 |
| 2 | 3 | 4 |
| 3 | 4 | 5 |
| 4 | 5 | 6 |
| 5 | 6 | 7 |
Black: given data. Blue: working we add.
Two independent fair spinners have numbers 1 to 2 and 1 to 3. Find the probability that their sum is at least 4.
| A \ B | 1 | 2 | 3 |
|---|---|---|---|
| 1 | 2 | 3 | 4 |
| 2 | 3 | 4 | 5 |
Black: given data. Blue: working we add.
Two independent fair spinners have numbers 1 to 3 and 1 to 3. Find the probability that their sum is at least 4.
| A \ B | 1 | 2 | 3 |
|---|---|---|---|
| 1 | 2 | 3 | 4 |
| 2 | 3 | 4 | 5 |
| 3 | 4 | 5 | 6 |
Black: given data. Blue: working we add.
Two independent fair spinners have numbers 1 to 4 and 1 to 3. Find the probability that their sum is at least 5.
| A \ B | 1 | 2 | 3 |
|---|---|---|---|
| 1 | 2 | 3 | 4 |
| 2 | 3 | 4 | 5 |
| 3 | 4 | 5 | 6 |
| 4 | 5 | 6 | 7 |
Black: given data. Blue: working we add.