Advanced · 15 min
Combining probabilities
Distinguish independent events from draws without replacement.
Multiply independent probabilities
For independent events, one event does not change the chance of the other. The probability that both happen is the product of their probabilities.
Worked example
Two fair independent coin tosses both give heads with probability 1/2 × 1/2 = 1/4.
Update after a draw
Without replacement, the first draw changes the available items. Use the updated counts when finding the probability of the second draw.
Worked example
From 3 red and 2 blue counters, P(two red without replacement) = 3/5 × 2/4 = 3/10.
Compare replacement rules
- Calculate the probability of two blue draws from a bag of 3 blue and 2 red counters when the first counter is replaced.
- Repeat without replacement and explain the change.