Question

What is the probability of getting a face card when a card is drawn from a pack of 52 cards
A). $${\displaystyle \frac{1}{13}}$$
B). $${\displaystyle \frac{2}{13}}$$
C). $${\displaystyle \frac{3}{13}}$$
D). $${\displaystyle \frac{1}{26}}$$

Answer 1

Hint: This problem is related to probability. In this we need to know the total numbers of cards and the total number of face cards. So that the ratio of total number of face cards to the total number of cards will be the probability. Also we should know what face cards are. They are the symbolized cards as J,Q,K in all four suites.

Complete step-by-step solution:
Given that we have to find the probability of getting a face card from a pack of 52 cards.
Now we know that in a deck of 52 cards there are four suits.
Each suite has 13 cards. And in those 13 cards there are 3 face cards: jack(J), queen(Q) and king(K).
Thus there are 12 face cards in total.
Thus we can find the probability as,
$$P(E)={\displaystyle \frac{\text{Number of face cards}}{\text{Total number of cards}}}$$
Now we will write the numbers in the above cards as,
$$={\displaystyle \frac{12}{52}}$$
Thus on dividing we get,
$$={\displaystyle \frac{3}{13}}$$
Thus the probability of getting the face card is $${\displaystyle \frac{3}{13}}$$.

Note: Here note that, we are asked the probability of overall face cards in a deck of 52 cards. If we are asked to find the probability of face cards in a particular suite then that will be $${\displaystyle \frac{3}{13}}$$ because the face cards in a suite are 3 and the number of cards in a suite is 13.
Also note that a particular face card can also be asked. Like there are 4 J,Q,K in a deck. So the probability of a particular face card is $${\displaystyle \frac{1}{13}}$$.