Question

From a pack of 52 playing cards all cards whose numbers are multiples of 3 are removed.A card is now drawn at random. Find the probability that card is:-
(i) a face card
(ii) an even numbered red card.

Answer 1

$$\begin{gathered} \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{cards}=52 \\ \mathrm{Multiples}\mathrm{of}3\mathrm{in}\mathrm{each}\mathrm{set}=3 \\ \mathrm{Multiples}\mathrm{of}3\mathrm{in}\mathrm{all}\mathrm{the}\mathrm{four}\mathrm{sets}=12 \\ \mathrm{Remaining}\mathrm{number}\mathrm{of}\mathrm{cards}=52-12=40 \\ \left(\mathrm{i}\right)\mathrm{Number}\mathrm{of}\mathrm{face}\mathrm{cards}\mathrm{in}\mathrm{each}\mathrm{set}=3 \\ \mathrm{Probability}\mathrm{that}\mathrm{the}\mathrm{card}\mathrm{drawn}\mathrm{is}\mathrm{a}\mathrm{face}\mathrm{card}(\mathrm{King},\mathrm{Jack}\mathrm{And}\mathrm{Queen})=12/40 \\ =3/10 \\ \left(\mathrm{ii}\right)\mathrm{Number}\mathrm{of}\mathrm{red}\mathrm{cards}=20\mathrm{Number}\mathrm{of}\mathrm{even}\mathrm{numbered}\mathrm{red}\mathrm{cards}\mathrm{in}20\mathrm{cards} \\ =10\mathrm{Probability}\mathrm{of}\mathrm{an}\mathrm{even}\mathrm{numbered}\mathrm{red}\mathrm{card} \\ =10/20 \\ =1/2. \end{gathered}$$