Question

The king, queen and jack of clubs are removed from a deck of $52$ playing cards and then well shuffled. One card is selected from the remaining cards. Find the probability of getting a heart.

Answer 1

Step 1 Finding the total number of outcomes and the number of favorable outcomes:

The event is the selecting a card from the pack.

There are ten of all four suits(Hearts, Diamonds, Spades, and Clubs) from which king, queen, and jack of clubs are removed.

$$\begin{gathered} TotalOutcome=Totalcards-(KingofClub+QueenofClub+JackofClub) \\ TotalOutcome=52-(1+1+1) \\ TotalOutcome=52-3 \\ TotalOutcome=49 \end{gathered}$$

So, the total number of outcomes is $49$.

Out of the total number of outcomes, the number of hearts is $13$.

So, the number of favorable outcomes is $13$.

Step 2 Finding the probability of getting the number number of hearts:

The formula for probability is,

$$\begin{gathered} \Rightarrow Probability=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes} \\ \therefore P(numberofhearts)=\frac{13}{49} \end{gathered}$$

Therefore, the probability of getting the number of hearts is $\frac{13}{49}$.