Question

One card is drawn from a well-shuffled deck of 52 cards. The probability of drawing an ace is
[a] $\dfrac{1}{12}$
[b] $\dfrac{1}{13}$
[c] $\dfrac{1}{50}$
[d] $\dfrac{3}{10}$

Answer 1

Hint: Probability of event E = $\dfrac{n(E)}{n(S)}=\dfrac{\text{Favourable cases}}{\text{Total number of cases}}$ where S is called the sample space of the random experiment. Assume E as the event of drawing out an ace when the random experiment is drawing a card from a well-shuffled deck of 52 cards. Find n (E) and n (S) and use the above formula to find the probability.

Complete step-by-step answer:

Before solving the question, we need to understand the composition of a deck of 52 cards.
The cards are of two colours Red and Black
Each colour has two suits.
Red suits are Diamond and heart
Black suits are Spade and Club.
Each suite has 13 ranks
Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King.
Now consider the random experiment of drawing a card from a well-shuffled deck of 52 cards.
Let E be the event: The card drawn is an ace.
Since there are 4 ace cards(one in each suite), we have favourable cases = 4
Hence, we have n (E) = 4
The total number of ways in which we can choose cards = 52
Hence, we have n(S) =52
We know that $P\left( E \right)=\dfrac{n\left( E \right)}{n\left( S \right)}$
Hence, we have
P (E) = $\dfrac{4}{52}=\dfrac{1}{13}$
Hence the probability that the drawn card is ace is $\dfrac{1}{13}$
Hence option [b] is correct.

Note: [1] It is important to note that drawing uniformly at random from a deck of well-shuffled cards is important for the application of the above problem. If the draw is not random or the deck is not well-shuffled, then there is a bias factor in drawing, and the above formula is not applicable. In those cases, we use the conditional probability of an event.