Follow the branches, choose the right paths and check your fractions.
| Complete path | First branch | Second branch | Multiply along path |
|---|---|---|---|
RR | R: 4/7 | R after R: 4/7 | 4/7 × 4/7 = 16/49 |
RB | R: 4/7 | B after R: 3/7 | 4/7 × 3/7 = 12/49 |
BR | B: 3/7 | R after B: 4/7 | 3/7 × 4/7 = 12/49 |
BB | B: 3/7 | B after B: 3/7 | 3/7 × 3/7 = 9/49 |
| First selection and remaining bag | Possible second selection and full result |
|---|---|
Red selected (4/7): 3 red and 3 blue remain | Another red: 4/7 × 3/6 = 2/7. A blue: 4/7 × 3/6 = 2/7. |
Blue selected (3/7): 4 red and 2 blue remain | A red: 3/7 × 4/6 = 2/7. Another blue: 3/7 × 2/6 = 1/7. |
Support and clarity
Straight answers to the questions people ask most often.
Yes. Use the later branch probability for what remains after the earlier result. Without replacement, copying the first-stage fractions into the second stage gives the wrong answer.
Sources and references
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