Solutions to Exercises#

  1. Half the numbers in the event set \(\{1,2,3,4,5,6\}\) are even.

  2. Let event set \(G\) represent drawing a green marble, and use set complements.

\[P(\bar G)=1-P(G)=1-\frac{4}{17}=\frac{13}{17}\]

  1. Using events sets \(F\) and \(B\) for face cards and black respectively, we use intersections and set complements. In every suit, there are 3 face cards and 10 non-face cards.

\[P(\bar F \cap B)=\frac{20}{52}\]

  1. Using event sets \(H\), \(E\) and \(A\), note that \(E\cap A=\emptyset\), so that \(E\cap \bar A=E\).

\[P(H\cap E \cap \bar A)=\frac{6}{52}=\frac{3}{26}\]