Question

What is the probability of getting a king or a queen in a single draw from a pack of 52 cards?
A.$\dfrac{1}{{26}}$
B. $\dfrac{1}{{13}}$
C. $\dfrac{2}{{13}}$
D. none

Answer 1

Calculate the total number of cards having king or a queen. We use the method for probability to find the probability of getting a king or a queen.

• Probability of an event is given by the number of possibilities divided by total number of possibilities.

Complete answer:
We know a deck contains 52 cards where there are 4 kings and 4 queens.
Total number of cards having king or a queen $= 4 + 4 = 8$
Now we find the probability of choosing a king card or a queen card from a deck of 52 cards.
Probability is given by dividing the number of cards to choose from by total number of cards available.
Probability $= \dfrac{8}{{52}}$
Writing the numerator and denominator in factored form
Probability $= \dfrac{{2 \times 4}}{{13 \times 4}}$
Cancel out the same terms from numerator and denominator.
Probability $= \dfrac{2}{{13}}$
Thus, probability of choosing one card from deck of 52 cards such that the card is a king or a queen is $\dfrac{2}{{13}}$or 0.15

$\therefore$Option C is correct.

Note:
Students should always check their answer of probability should be less than or equal to one and greater than or equal to zero. Students many times try to solve the combination formula by opening the factorial but that makes the solution complex instead try to cancel out as many factorial terms as you can from numerator and denominator. Many students try to apply a combination method which is not required here as we don’t have to choose and it is specified that we have to draw a card in a single draw so we don’t have to check if it will be king or queen it can be any card.