Let A,B,C be three events, and let X=IA, Y=IB, and Z=IC be the associated indicator random variables.

Question

We already know that X⋅Y is the indicator random variable of the event A∩B. In the same spirit, give an algebraic expression, involving X,Yand Z, for the indicator random variable of the following events.

Note: Express your answers in terms of X,Y, and Z (the answer box is case sensitive) using standard notation.

1. The event A^c∩B∩C.

2. At most two of the events A,B,C occurred.

Answer 1

I have posted 7 Probability questions and i am willing to pay $ for the solution.