Question

A card is drawn at random from a pack of well shuffled deck playing cards. Find the probability of i) King or Jack ii) spade or ace

Answer 1

$$\begin{gathered} \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{cards}\mathrm{in}\mathrm{a}\mathrm{deck}=52 \\ \mathrm{Total}\mathrm{possible}\mathrm{outcomes}=52 \\ \left(1\right). \\ \mathrm{Number}\mathrm{of}\mathrm{Kings}=4 \\ \mathrm{Number}\mathrm{of}\mathrm{Jacks}=4 \\ \mathrm{number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}=4+4=8 \\ \mathrm{p}\left(\mathrm{getting}\mathrm{King}\mathrm{or}\mathrm{Jack}\right)=\frac{\mathrm{number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{possible}\mathrm{outcomes}}=\frac{8}{52}=\frac{2}{13} \\ \left(2\right). \\ \mathrm{Number}\mathrm{of}\mathrm{spades}=13 \\ \mathrm{Number}\mathrm{of}\mathrm{aces}=4 \\ \mathrm{Number}\mathrm{of}\mathrm{ace}\mathrm{of}\mathrm{spade}=1 \\ \mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}=13+4-1=16 \\ \mathrm{p}\left(\mathrm{getting}\mathrm{Spade}\mathrm{or}\mathrm{an}\mathrm{ace}\right)=\frac{\mathrm{number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{possible}\mathrm{outcomes}}=\frac{16}{52}=\frac{4}{13} \end{gathered}$$