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.