Solution: 2015 Winter Final - 13

Author: Michiel Smid

Question

Consider three events, $A$, $B$, and $C$ in a sample space $S$. Is the following true or false?

$\Pr\bigl(A \cup (\overline{B} \cap \overline{C})\bigr) = $

$\Pr(A) + \Pr(B)\ - $ $\Pr(C).$

(a)

False

(b)

None of the above.

(c)

True

$ Pr(A \cup (\overline{B} \cap \overline{C})) = Pr(A) + Pr(B) - Pr(C) $.

I would honestly need to draw it out to prove it’s false