Compound & Conditional Probability
Multiply for 'and' (adjusting for no replacement), and add for 'or'.
The rules
- Without replacement, the second probability changes.
- P(A and B) = P(A) · P(B given A).
- P(A or B) = P(A) + P(B) − P(A and B).
- Conditional: use the new, smaller group.
Watch out: Forgetting that the total goes down without replacement.
Worked example
Two cards are drawn without replacement from a deck of 10 numbered 1 to 10. What is the probability that both are even?
- (5/10) · (4/9).
- = 20/90 = 2/9.
Answer: 2/9
Try it yourself
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