Question

What is the probability of not picking a face card when you draw a card at random from a pack of $ 52 $ cards?
A. $ \dfrac{1}{{13}} $
B. $ \dfrac{4}{{13}} $
C. $ \dfrac{{10}}{{13}} $
D. $ \dfrac{{12}}{{13}} $

Answer 1

Hint: As we know that probability is the prediction of a particular outcome of a random event. It is a set of all the possible outcomes for a random experiment. We can calculate the question with the formula of probability i.e. Probability $ = \dfrac{{No.\,\,of\,favourable\,\,outcomes}}{{Total\,\,number\,\,of\,\,outcomes}} $ . There are total $ 52 $ cards in a deck. So we have the total number of outcomes $ = 52 $ .

Complete step-by-step answer:
We have the total number of cards $ = 52 $ .
We know that in a deck of $ 52 $ cards, there are total $ 12 $ face cards.
So we can calculate the total number of non-face cards i.e. Total cards $ - $ Face cards. It gives us $ 52 - 12 = 40 $ .
So now we have total number of non- face cards or number of favourable outcomes $ = 40 $
No, by putting the values in the formula we have Probability $ = \dfrac{{40}}{{52}} $ . It gives us $ \dfrac{{10}}{{13}} $ .
Hence the correct option is (c) $ \dfrac{{10}}{{13}} $ .
So, the correct answer is “Option C”.

Note: We should be careful that we have to find the probability of a non-face card, so we have to subtract it. If we have to find the probability of a face card then we have the value $ \dfrac{{12}}{{52}} $ , as there are total $ 12 $ face cards. So it gives the value $ \dfrac{3}{{13}} $ . Before solving this kind of question we should have the clear idea of the number of cards and how to calculate them. We should also note that ace is not a face card.