**Question: Let Ai be any events. **

**a) Show that P(A1 ∩A2 ∩A3) = P(A1 ∩A2 ∩A3) = P(A1)·P(A2 | A1)·P(A3 | A1 ∩A2) . **

**b) Generalize this to give a formula for the intersection of any number of events. [Hint: Use induction.]**

**Solution: **

Skip to content
# Let Ai be any events. a) Show that P(A1 ∩A2 ∩A3) = P(A1 ∩A2 ∩A3) = P(A1)·P(A2 | A1)·P(A3 | A1 ∩A2)

Students Helping Clan

**Question: Let Ai be any events. **

**a) Show that P(A1 ∩A2 ∩A3) = P(A1 ∩A2 ∩A3) = P(A1)·P(A2 | A1)·P(A3 | A1 ∩A2) . **

**b) Generalize this to give a formula for the intersection of any number of events. [Hint: Use induction.]**

**Solution: **