C chengeto New member Joined Feb 28, 2009 Messages 49 Oct 14, 2009 #1 \(\displaystyle P(B \prime \cup C)= P(1-P(B)) + P(C) - P ( B \cap C)\) I am in the right direction trying to find the probability of compliment B union C ?
\(\displaystyle P(B \prime \cup C)= P(1-P(B)) + P(C) - P ( B \cap C)\) I am in the right direction trying to find the probability of compliment B union C ?
pka Elite Member Joined Jan 29, 2005 Messages 11,978 Oct 15, 2009 #2 \(\displaystyle \begin{array}{rcl} {P(B' \cup C)} & = & {P(B') + P(C) - P(B' \cap C)} \\ {} & = & {1 - P(B) + P(C) - \left[ {P(C) - P(B \cap C)} \right]} \\ {} & = & {1 - P(B) + P(B \cap C)} \\ \end{array}\)
\(\displaystyle \begin{array}{rcl} {P(B' \cup C)} & = & {P(B') + P(C) - P(B' \cap C)} \\ {} & = & {1 - P(B) + P(C) - \left[ {P(C) - P(B \cap C)} \right]} \\ {} & = & {1 - P(B) + P(B \cap C)} \\ \end{array}\)
