Conditional probability
Conditional probability (Extended)
- Conditional probability is the chance of one event given that another has already happened.
- Read it by looking only at the part that matches the condition — on a Venn diagram, two-way table or tree.
Practice
Conditional probability is the probability of an event:
It is the probability of B given that A has occurred.
Worked example
- In a class of $30$, $18$ study French; of those, $7$ also study German.
- A French student is picked. Look only at the $18$ French students:
$$\text{P}(\text{German} \mid \text{French}) = \frac{7}{18}$$
Practice
Of 18 French students, 7 also study German. P(German | French) = 7/a. What is a?
Given they are French, the total to divide by is the 18 French students.
Practice
Of 20 students, 12 like tea; of those, 3 also like coffee. P(coffee | tea) = 3/a. What is a?
Condition on the 12 tea-drinkers, so a = 12.
You've got it
Key idea
- conditional probability = chance of $B$ given $A$ already happened
- restrict your attention to just the group that meets the condition
- $\text{P}(\text{German} \mid \text{French}) = \dfrac{7}{18}$ (out of the French students only)