Question

The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of (1) heart (2) queen and (3) a club.

Answer 1

Hint: Probability is nothing but a ratio; number of favourable cases to number of total cases. In order to get this ratio, we’ll count the total cases first then we’ll go for the number of favourable cases. Favourable cases are what we have asked in the question.

Complete step-by-step answer:
First, we’ll find the total number of cases because this will be the same for all the cases.
We know there are 4 clubs and king, queen and jack are present in each card. So 3x4=12 total face cards.
The question said the king, queen and jack of the club are removed from the deck. So, we’ll left with 52-3=49 total cards. These 49 cards will be our total cases.
Now,
(1). Getting a heart
We know there are 13 cards of heart and since cards are removed from the club so no cards are removed from hearts. If we consider getting a heart as an event then all 13 cases will be in our favour. Hence the required probability will be
$\begin{gathered}
  \dfrac{{{\text{Number of favorable cases}}}}{{{\text{Number of total cases}}}} \\
   = \dfrac{{13}}{{49}} \\
\end{gathered} $
Hence the probability of getting a heart is $\dfrac{{13}}{{49}}$.
(2). Getting a queen
We know there are 4 queens in a deck; one in each club. If we consider getting a queen as an event then the number of favourable cases will be 3, not 4 because 1 queen is removed from the club.
Hence the probability will be
$\begin{gathered}
  \dfrac{{{\text{Number of favorable cases}}}}{{{\text{Number of total cases}}}} \\
   = \dfrac{3}{{49}} \\
\end{gathered} $
Hence the probability of getting a queen is $\dfrac{3}{{49}}$.
(3). A club
We know that there are 13 cards of the club. After removing the king, queen and jack of the club only 10 club cards are left in the deck. So, the favourable cases will be 10 and the probability will be
$\begin{gathered}
  \dfrac{{{\text{Number of favourable cases}}}}{{{\text{Number of total cases}}}} \\
   = \dfrac{{10}}{{49}} \\
\end{gathered} $
Hence the probability of getting a club will be $\dfrac{{10}}{{49}}$


Note:The standard pack of 52 playing cards includes 4 clubs which are heart, diamond, clubs and spades. Spades and clubs used to be of black colour and the rest of two is of red colour. There are 13 cards of each club. This set also includes face cards. Which are three of each club in number. One joker, one king and one queen.