Question

From a pack of 52 playing cards, all cards whose numbers are multiples of 3 are removed. a card is now drawn in random. What is the probability that the card drawn is

i) A face card (King, Queen or Jack)

ii) an even numbered red card?

Answer 1

$$\begin{gathered} Totalnumberofcardsinadeck=52 \\ cardswhicharemultipleofthreeare3,6,9 \\ Thesecardsareremoved,sototal3\times 4=12cardsareremoved. \\ Leftcardsare52-12=40cards \\ facecardsinadeckareking,queen,jackinallfoursuits. \\ Sototalnumberoffacecards=3\times 4=12 \\ 1)Sotheprobabilityofdrawingfacecardis\frac{12}{40}=\frac{3}{10}ans \\ Evennumberedcardsinredsuitare2,4,8,10. \\ Sothetotalnumberofevennumberedredcardsare4\times 2=8 \\ 2)Sotheprobabilityofdrawingevennumberedredcards=\frac{8}{40}=\frac{1}{5}Ans \end{gathered}$$