# Probability of three independent events.

Let the three independent events $A, B,$ and $C$ be such that $P(A)=P(B)=P(C)= \frac14.$ find $P[(A^*\cap B^*) \cup C].$

My solution starts from using the probability of their complements which is $\frac34$, I do not know how to answer this question. Please help.

• Hi Jonarie - It's considered polite on this site to share what you've thought about and tried, and to formulate your question as a question rather than seeming like a textbook exercise. – Ben Blum-Smith Oct 4 '14 at 3:24
• Hi.. thanks for the reminder – Jonarie Ramos Vergara Oct 4 '14 at 3:48
• Also asked at stats.stackexchange.com/q/117821/10259 – Joel Reyes Noche Oct 8 '14 at 4:00

The general idea here being that, if $A$ and $B$ are independent, then:
1. $P(A \cap B) = P(A)P(B)$
2. $P(A \cup B) = P(A) + P(B) - P(A \cap B) = P(A \cup B) = P(A) + P(B) - P(A)P(B)$
And of course $P(A^*) = 1-P(A)$.