Question

A small pack of cards consists of the Ace, King, Queen, Jack and ten of all four suits. Find the probability of selecting from this pack the Queen of spades.

Answer 1

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

There are Ace, King, Queen, Jack, and ten of all four suits.

$$\begin{gathered} TotalOutcomes=4\times [Ace+King+Queen+Jack+10] \\ =4\times [1+1+1+1+1] \\ =4\times 5 \\ \therefore TotalOutcomes=20 \end{gathered}$$

There is only $1$ Queen of spades.

So, the number of favorable outcomes is $1$.

Step 2 Finding the probability of getting Queen of spades:

$$\begin{gathered} Probability=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes} \\ \therefore P(Queenofspades)=\frac{1}{20} \end{gathered}$$

Therefore, the probability of getting Queen of spades is $\frac{1}{20}$.