Question

a card is drawn at random from a well shuffled deck of playing cards. find the probability that the card drawn is:
1. a card of heart or a king.
2. neither an ace nor a jack

Answer 1

$$\begin{gathered} \mathrm{a}) \\ \mathrm{There}\mathrm{are}\mathrm{total}52\mathrm{card}\mathrm{with}13\mathrm{card}\mathrm{of}\mathrm{each}\mathrm{heart},\mathrm{diamond},\mathrm{spade},\mathrm{club}. \\ 4\mathrm{kind},4-\mathrm{queen},4-\mathrm{jack},4-\mathrm{ace} \\ \mathrm{So}\mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{heart}=\frac{13}{52}=\frac{1}{4} \\ \mathrm{and}\mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{king}=\frac{4}{52}=\frac{1}{13} \\ \mathrm{So}\mathrm{Required}\mathrm{probability}=\frac{1}{4}\times \frac{1}{13}=\frac{1}{52} \\ \mathrm{b}) \\ \mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{aace}=\frac{4}{52}=\frac{1}{13} \\ \mathrm{and}\mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{jack}=\frac{4}{52}=\frac{1}{13} \\ \mathrm{So}\mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{jack}\mathrm{or}\mathrm{ace}=\frac{1}{13}\times \frac{1}{13}=\frac{1}{169} \\ \mathrm{So}\mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{neither}\mathrm{jack}\mathrm{nor}\mathrm{ace}=1-\frac{1}{169}=\frac{168}{169} \end{gathered}$$