Conditional probability, independent events and tree reasoning.
Example 1
A bag contains 3 red and 6 blue counters. Two are drawn without replacement. Find the probability both are red.
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Answer: 726
- First red: 93.
- Then red: 82.
- Multiply: 726.
Example 2
Of 13 students, 10 study French and 5 study both French and music. Given that a student studies French, find the probability they study music.
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Answer: 105
- Restrict the sample space to the 10 French students.
- 5 of those study music, so P(music ∣ French)=105.
Example 3
Independent events A and B have P(A)=21 and P(B)=51. Find P(A∩B).
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Answer: 101
- For independent events, P(A∩B)=P(A)P(B).
- Multiply: (21)(51)=101.