Question

A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is
\[\begin{align}
  & A.\dfrac{1}{13} \\
 & B.\dfrac{2}{13} \\
 & C.\dfrac{1}{26} \\
 & D.\dfrac{1}{52} \\
\end{align}\]

Answer 1

Hint: In this question, we need to find the probability of getting a queen of the club or a king of heart. For this, we will first understand the type of cards in a deck. Then we will find our required cards which will be our favorable outcome. The total outcome will be the total number of cards which is 52. Using the formula $ \text{Probability}=\dfrac{\text{Number of favorable outcomes}}{\text{total outcomes}} $ we will find our required probability.

Complete step by step answer:
Here we are given a deck of cards which has 52 cards. We need to find the probability of picking a queen of club or king of heart out of the deck. For this, let us first understand the type of cards in a deck.
In a deck of cards, we have 13 numbers, i.e, 2, 3, 4, 5, 6, 7, 8, 9, J, Q, K, A, and we have four suits which are club, spade, heart, and diamond. Every suite has 13 numbers as mentioned earlier. So there are $ 13\times 4=52 $ cards.
Here we need to find the number of cards for a queen of the club or a king of heart.
We have 4 queens but only one queen of the club.
We have 4 kings but only one king of heart.
So our favorable outcomes are 2 only.
Now as the total number of cards in a deck is 52 so we have a total outcome of 52.
Hence a number of favorable outcomes = 2.
A number of total outcomes = 52.
We know $ \text{Probability}=\dfrac{\text{Number of favorable outcomes}}{\text{total outcomes}} $ .
So we have $ \text{Probability}=\dfrac{\text{2}}{\text{52}} $ .
Dividing the numerator and the denominator by 2 we get $ \text{Probability}=\dfrac{\text{2}\div \text{2}}{\text{52}\div \text{2}}=\dfrac{1}{26} $ .
Hence our required probability is $ \dfrac{1}{26} $ .
Hence option C is the correct answer.

Note:
 Students should note that we need to consider every possibility before submitting the final answer. Make sure that the probability is in the simplest form. Students should keep in mind the types of cards in a deck. Note that probability should always lie between 0 and 1.