Question & Answer

What is the probability of getting a king or a queen in a single draw from a pack of 52 cards?
A. $\dfrac{1}{26}$
B. $\dfrac{1}{13}$
C. $\dfrac{2}{13}$
D. None

ANSWER Verified Verified
Hint: The event of getting a king or queen from a pack of 52 cards is required for solving this problem. We first have to evaluate the sample space of the particular event and then find the favourable outcome from the sample space. By taking the ratio of these events, we evaluate the probability. We follow the same methodology for solving the question.

Complete Step-by-Step solution:
In mathematics, the possibility of occurrence of an event falls under the category of probability. If a random experiment is performed, then each of its outcomes is known as an elementary event. The set of all possible outcomes of a random experiment is called the sample space associated with it and it is generally denoted by ‘S’.
According to this problem, the total number of cards in the deck$=52$.
Now, there are 4 kings and 4 queens in total out of the 52 cards available in the deck.
Therefore, number of kings$=4$
Also, number of queens$=4$
Number of favourable outcomes of drawing a king or queen from the deck of cards $=8$.
Total number of outcomes $=52$.
P (occurrence of the event) $=\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
Therefore, by using the above formula, P (getting a king or queen) $=\dfrac{8}{52}=\dfrac{2}{13}$.
Hence, the probability of getting a king or queen is $\dfrac{2}{13}$.
Therefore, option (c) is correct.

Note: The key concept for solving a problem is the knowledge of probability of occurrence of an event. Students must be careful while calculating the space for favorable events. There should be no redundancy of particular events in the favorable outcomes.