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
(a) $\dfrac{1}{13}$
(b) $\dfrac{1}{26}$
(c) $\dfrac{1}{52}$
(d) $\dfrac{1}{4}$

Answer 1

Hint: At first count the total number of favourable outcomes which is 2 and use it as n(E). Then count the event that can occur possibly in sample space which is 52. Then use the formula $P\left( E \right)=\dfrac{n\left( E \right)}{n\left( S \right)}.$

Complete step-by-step answer:
In the question we are given a pack of 52 cards and we have to find the probability of getting a queen of club or a king of heart.

At first we will define what probability is and understand the basic terms related to the probability to be used in the question.

The probability of an event is a measure of the likelihood that the event would occur.

If an experiment’s outcomes are equally likely to occur, then the probability of an event E is the number of outcomes in E divided by the total number of outcomes in the sample space.

Here sample space consists of all the events that can occur possibly.

So, it can be written as, $P\left( E \right)=\dfrac{n\left( E \right)}{n\left( S \right)}$
Here, P(E) is the probability of an event or events which is asked, n(E) is the number of favourable events and n(S) is the number of all the events that can occur possibly.

Now we have to know about the cards too about which question is asked.

In a pack of 52 cards there are four suits available such as Spade, Heart, Club, and Diamond. All have 13 cards each. Each suit has 1 King, 1 Queen, 1 Jack, 1 Ace and 9 cards number 2-10.

So here we are asked to find the probability of getting a queen of a club or a king of heart.

So the sample space consists of all the 52 cards in the pack.

So, n(s) = 52.

Now for the number of favourable events a queen of club or king of heart is only 2.
So n(E)=2

So the probability is,

$\begin{align}
  & P\left( E \right)=\dfrac{n\left( E \right)}{n\left( S \right)} \\
 & P\left( E \right)=\dfrac{2}{52}=\dfrac{1}{26} \\
\end{align}$

Hence the probability is $\dfrac{1}{26}$ .

Therefore, the correct answer is option (b).


Note: There is another way of doing this problem which is first getting the probability of getting the queen of club and queen of heart separately which are $\dfrac{1}{52}$ and $\dfrac{1}{52}$ respectively.

Now adding the probability of two events $\dfrac{1}{52}+\dfrac{1}{52}=\dfrac{1}{26}$
Hence we got the answer.