Question

From a pack of $ 52 $ cards one card is drawn at random, the probability that it is either a king or queen is
$
  1)\;\dfrac{1}{{13}} \\
  2){\text{ }}\dfrac{2}{{13}} \\
  3)\;\dfrac{3}{{13}} \\
  4){\text{ }}\dfrac{4}{{13}} \\
$

Answer 1

Hint: Probability can be defined as the ratio of the favorable outcomes to the total possible outcomes. Here we will find the total of possible outcomes for king and queen and then will take its ratio with the total number of the possible outcomes in the pack of $ 52 $ cards.

Complete step by step solution:
Let us assume that the A be an event that card drawn random is either a king or queen
We know that the deck of cards has four sets of each card and therefore there are four kings or queens in a deck.
Therefore, total number of cards of kings and queens $ = 4 + 4 = 8 $
Therefore, favorable outcomes for the event A is $ n(A) = 8 $
The total possible outcomes for the pack of $ 52 $ cards, $ n(S) = 52 $
Now, the formula of finding the probability can be given by –
Probability can be defined as the ratio of the favorable outcomes with the total number of possible outcomes.
Probability, $ P(A) = \dfrac{{n(A)}}{{n(S)}} $
Place the values in the above expression –
 $ P(A) = \dfrac{8}{{52}} $
Find the factors for the terms in the above expression –
 $ P(A) = \dfrac{{4 \times 2}}{{4 \times 13}} $
Common factors from the numerator and the denominator cancel each other and therefore remove from the above expression.
 $ P(A) = \dfrac{2}{{13}} $
From the given multiple choices, option B is the correct answer.
So, the correct answer is “Option B”.

Note: Always remember that to know the correct probability one should consider all the possible favorable outcomes and cross check it. The range of the probability always lies between zero and one. When the probability consists of or adds the terms and when it contains and finds the terms common in both.