Question

Given a group of events A1, A, ..., An, use interaction, unions, and complements to express (a) none of them occur (b) only A1 and A2 occur.

Answer 1

a) The event that at least one them occur is the union of the events A1, A2,...., An. The complement of this will give the event in which none of them occur

The event that none of them occur = (A1 U A2 U A3 ......U An)^c

b) only A1 and A2 occur when the events A3 to An wont occur and A1 and A2 occur

Event that only A1 and A2 occur = (A3 U A4 U A5....U An)^c$\cap$ (A1 $\cap$ A2)