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 any King or Queen.

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 Ace, King, Queen, Jack, and ten of all four suits including Ace(Hearts, Diamonds, Spades, and Clubs).

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

So, the total number of outcomes is $20$.

Out of the total number of outcomes, the number of cards(any King or Queen) is $2$ in all four suits.

$$\begin{gathered} Numberofcards(anyKingorQueen)=4\times 2 \\ Numberofcards(anyKingorQueen)=8 \end{gathered}$$

So, the number of favorable outcomes is $8$.

Step 2 Finding the probability of getting the King or Queen card:

The formula for probability is,

$$\begin{gathered} \Rightarrow Probability=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes} \\ \Rightarrow P(KingorQueencard)=\frac{8}{20} \\ \therefore P(KingorQueencard)=\frac{2}{5} \end{gathered}$$

Therefore, the probability of getting the King or Queen card is $\frac{2}{5}$.