Question

A card is drawn at random from a pack of well-shuffled 52 playing cards. What is the probability that the card drawn is neither king nor a queen?

Answer 1

Hint : The number of king and queen cards are subtracted from the total number of cards, this will be the favorable outcome as it shows that the chosen card will neither be king nor a queen.
Formula of probability:
$P = \dfrac{f}{T}$ where,
P = Probability
F = Favorable outcomes
T = Total outcomes

** Complete step-by-step answer** :
King and queen cards are known as the face cards.
Each face card is present in each suit and we have 4 suits, thus:
Number of king cards = 4
Number of queen cards = 4
Number of cards left after deleting both king and queen cards:
$\Rightarrow$ 52 – (4 + 4)
$\Rightarrow$ 52 – 8 = 44 ___________ (1)
Calculating the required probability:
Favorable outcomes (f) = Cards without the kings and queens (so the chosen card is neither king nor queen)
= 44 [from (1)]
Total outcomes (T) = Total number of cards
= 52
Applying the formula of probability:
$\Rightarrow P = \dfrac{f}{T}$
Substituting the values, we get:
$\Rightarrow P = \dfrac{{44}}{{52}} \\\ \Rightarrow P = \dfrac{{11}}{{13}} \\\$
Therefore, if a card is drawn at random from a pack of well-shuffled 52 playing cards, the probability that the card drawn is neither king nor a queen is $\dfrac{{11}}{{13}}$

Note : We have a total of 3 face cards (king, queen and jack) in each of the four suits, so total number of face cards present are:
3 X 4 = 12
The sum of probabilities of happening and non-happening of an event is always equal to 1.