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 spade?

Answer 1

Hint: The total number of spade cards present in the deck will be our favorable outcomes which can be substituted in the formula of probability so as to calculate the required probability.
Formula of probability:
 $ P = \dfrac{f}{T} $ where,
P = Probability
F = Favorable outcomes
T = Total outcomes

Complete step-by-step answer:
Spade comes under the category of suit among the cards.
There are total 4 suits, so number of spade cards can be given as:
 $ \Rightarrow \dfrac{{52}}{4} $ = 13 (since there are 52 total cards)
Calculating the required probability:
Favorable outcomes (f) = Total number of spade cards
 = 13
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{{13}}{{52}} \\
\Rightarrow P = \dfrac{1}{4} \\
  $
Therefore, if a card is drawn at random from a pack of well-shuffled 52 playing cards, the probability that the card drawn is spade is $ \dfrac{1}{4} $

Note: In a deck of 52 cards, we have 4 kinds of suits namely clubs, spades, hearts and diamonds.
There are 13 cards belonging to each suit.
As half the cards are red and half are black, among the suits:
spades and clubs are black while the hearts and clubs are red in color.
If an event has 0 probability, the event is impossible to occur while with probability 1, the event will surely occur.