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Year 10 · Statistics & Probability
Probability without replacement
For two events in a row, multiply the probabilities. Without replacement, the second probability changes.
How to do it
- Write the probability of the first event.
- Update the counts, then write the second.
- Multiply. "At least one" is 1 minus "none".
Worked example
A bag has 5 red and 3 blue counters. Two are taken out without replacement. What is the probability both are red?
First pick: 5/8. Then one fewer red and one fewer counter: 4/7. Multiply: 5/14.
Answer: 5/14
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Watch outAfter taking one out, both the top and the bottom change.
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