Practice question · Numerical answer
Events A and B satisfy P(A and B) = 0.12 and P(B) = 0.3. Compute P(A given B).
Hints
- Conditioning on B restricts attention to the outcomes where B holds.
- Divide the joint probability by the probability of the condition.
Show the answer
0.4 (answers within ±0.005 count)
Why
P(A given B) = 0.12/0.3 = 0.4. The denominator is the condition, never the other event: dividing by P(A) instead answers a different question. Conditioning rescales the shrunken sample space back to a total of 1.
Practise Conditional Probability and Independence
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