Question

If a card is randomly chosen from a pack of playing cards.

a) What is the probability of getting a king?

b) What is the probability of getting a number card?

c) What is the probability of getting a red card?

d) What is the probability of getting 4 of hearts?

Answer 1

$$\begin{gathered} \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{cards}\mathrm{in}\mathrm{a}\mathrm{deck}=52 \\ \mathrm{Total}\mathrm{possible}\mathrm{outcomes}=52 \\ \left(\mathrm{a}\right). \\ \mathrm{No}.\mathrm{of}\mathrm{kings}=4 \\ \mathrm{no}.\mathrm{of}\mathrm{favorable}\mathrm{outcomes}=4 \\ \mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{king}=\frac{\mathrm{no}.\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{possible}\mathrm{outcomes}}=\frac{4}{52}=\frac{1}{13} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{b}\right). \\ \mathrm{Number}\mathrm{of}\mathrm{number}\mathrm{cards}=36 \\ \mathrm{number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}=36 \\ \mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{number}\mathrm{card}=\frac{\mathrm{no}.\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{total}\mathrm{possible}\mathrm{outcomes}}=\frac{36}{52}=\frac{9}{13} \\ \left(\mathrm{c}\right).\mathrm{number}\mathrm{of}\mathrm{red}\mathrm{cards}=26 \\ \mathrm{number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}=26 \\ \mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{red}\mathrm{card}=\frac{\mathrm{no}.\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{total}\mathrm{possible}\mathrm{outcomes}}=\frac{26}{52}=\frac{1}{2} \\ \left(\mathrm{d}\right). \\ \mathrm{number}\mathrm{of}4\mathrm{of}\mathrm{hearts}=1 \\ \mathrm{number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}=1 \\ \mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{number}\mathrm{card}=\frac{\mathrm{no}.\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{total}\mathrm{possible}\mathrm{outcomes}}=\frac{1}{52} \end{gathered}$$