Question

A pack of cards consists of the Ace, King, Queen, Jack and ten of all the four suits. Find the probability of selecting an Ace.

Answer 1

Hint: Figure out the total number of cards in a deck before moving forward with the solution of the problem. There is an Ace in each suit and there are four suits in a deck. Take the ratio of the number of aces and the total number of cards in a deck to calculate probability.

Complete step-by-step answer:
Let us first understand the question properly. In a deck, there are total $52$ cards in which $26$ are of black colour and $26$ red colour. Out of which in each of the four suits of Spades, Hearts, Diamonds, and Clubs. (Diamonds and Hearts are of red colour cards while Spades and Clubs are of black colours.)

Each suit contains $13$ cards: $2,3,4,5,6,7,8,9,10$, Jack, Queen, King and Ace.

Now let’s understand the concept of probability. Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true. It is simply how likely something is to happen. And the probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
$ \Rightarrow \operatorname{Probability} = \dfrac{Favourable outcomes}{Total outcomes}$
Since we already know that, there are a total of four Ace in a pack of cards and the total number of cards is $52$.
$ \Rightarrow $ Required Probability$ = \dfrac{4}{{52}} = \dfrac{1}{{13}}$
Therefore, the probability of pick an Ace from the deck is $\dfrac{1}{{13}}$

Note:For solving problems associated with the deck of playing cards, you need to properly understand the working and concepts of a deck of cards. Do not forget to change the probability into its simplest fraction form or in decimals. An alternative approach can be taken to count the favourable outcomes and that will also lead you to the same formula.