Question

What is the probability of getting a court card (King, Queen and Knave) from a deck of 52 playing cards?
A. \[\dfrac{3}{{73}}\]
B. \[\dfrac{2}{{13}}\]
C. \[\dfrac{3}{7}\]
D. \[\dfrac{3}{{13}}\]

Answer 1

Hint: First of all, find the total number of outcomes and then find the total number of possible outcomes i.e., the number of outcomes of getting a court card (King, Queen and Knave). So, use this concept to reach the solution of the given problem.

Complete step-by-step solution -
Let E be the event of getting a court card (King, Queen and knave).
The total number of playing cards = 52
Hence the total number of outcomes = 52
We know that,
The number of king cards = 4
The number of Queen cards = 4
The number of Knave cards = 4
So, the total number of court cards (King, Queen and knave) = 4 + 4 + 4 = 12
Hence the total number of possible outcomes = 12
We know that the probability of an event is given by \[P\left( {\text{E}} \right) = \dfrac{{{\text{Total number of possible outcomes}}}}{{{\text{Total number of outcomes}}}}\]
\[
   \Rightarrow P\left( {\text{E}} \right) = \dfrac{{12}}{{52}} \\
  \therefore P\left( E \right) = \dfrac{3}{{13}} \\
\]
Thus, the correct option is D \[\dfrac{3}{{13}}\].

Note: The number of possible outcomes is always greater than or equal to the total number of outcomes. The probability of an event is always less than or equal to one and greater than or equal to zero.