Question

A card is drawn from a pack of 52 cards. What is the probability that it is the red queen?
A). \[\dfrac{1}{{26}}\]
B). \[\dfrac{1}{{13}}\]
C). \[\dfrac{1}{{52}}\]
D). \[\dfrac{2}{{13}}\]

Answer 1

Hint: We know that in a deck of 52 cards there are face cards also along with the number cards. Queen is one of the face cards. There are four queens. Two are black and two are red.so the probability of the red queen card is given by the ratio of total number of red queen cards to the total number of cards.

Complete step-by-step solution:
Given is a deck of 52 cards. So the total number of cards is 52.
Now in the deck there are four suites. Each suite has 13 cards.
The face card with Q written is the queen card.
There are four queens in a deck.
Heart and diamond are red in color whereas spades and clubs are in black.
So the total red queen cards are 2.
Thus the probability is given now by the ratio,
\[P(queen) = \dfrac{\text{Total red queen cards}}{\text{Total number of cards}}\]
\[P(queen) = \dfrac{2}{{52}}\]
On simplifying the ratio,
\[P(queen) = \dfrac{1}{{26}}\]
Thus this is the probability of getting a red queen.

Note: Note that if they ask us for particular red queen that is of either diamond or or heart then we will write the probability as \[P(queen) = \dfrac{1}{{52}}\] because there exist only one red heart queen and only one red diamond queen.