Question

One card is drawn from a well-shuffled deck of 52 cards. The probability that the card will not be an ace is:
 $
  {\text{A}}{\text{. }}\dfrac{1}{{13}} \\
  {\text{B}}{\text{. }}\dfrac{1}{4} \\
  {\text{C}}{\text{. }}\dfrac{{12}}{{13}} \\
  {\text{D}}{\text{. }}\dfrac{3}{4} \\
 $

Answer 1

Hint: In order to find the probability that the card will not be an ace, we first find out how many aces are there in a deck of 52 cards in order to compute its possibilities. Then we find the total number of possibilities and substitute these quantities in the formula of probability to determine the answer.

Complete step-by-step answer:
Given Data,
Deck of 52 cards
Ace
Firstly, a deck of 52 cards has four sets of 13 cards each representing four different symbols. Each symbol has an Ace in its 13 cards. So there are 4 aces in total in the deck.
Now the probability of an event not happening = 1 – the probability of an event happening.
As the total probability of an even is always equal to 1.
Therefore the probability of the card will not be an ace = 1 – the probability of the card being an ace.
The probability of the card being an ace is:
Number of favorable outcomes = 4 (there are 4 aces in total)
Total outcomes = 52 (total number of cards)
We know the formula of probability is, $ {\text{P = }}\dfrac{{{\text{favorable outcomes}}}}{{{\text{total outcomes}}}} $
Hence, P (A) = $ \dfrac{4}{{52}} $
Therefore the probability of not getting an ace = 1 – P (A)
 $ \Rightarrow {\text{P}}\left( {{\text{not ace}}} \right) = 1 - \dfrac{4}{{52}} $
 $ \Rightarrow {\text{P}}\left( {{\text{not ace}}} \right) = \dfrac{{48}}{{52}} $
 $ \Rightarrow {\text{P}}\left( {{\text{not ace}}} \right) = \dfrac{{12}}{{13}} $
So, the correct answer is “Option A”.

Note: In order to solve this type of problems the key is to first have a good idea about how a deck of 52 cards is arranged and what constitutes it. Once we know this we can calculate the number of possibilities of each of the given in the question and substitute them in the formula of probability. The total probability of an event is always exactly equal to 1, neither more than 1 nor less than 1.