Question

A card is drawn from a pack of 52 cards. The probability of getting a queen of clubs or a king of hearts is
(a) \[\dfrac{1}{{13}}\]
(b) \[\dfrac{2}{{13}}\]
(c) \[\dfrac{1}{{26}}\]
(d) \[\dfrac{1}{{52}}\]

Answer 1

Hint:
Here, we need to find the probability of getting a queen of clubs or a king of hearts. First, we will find the total number of cards in the pack. Then, we will find the number of queen of clubs and king of hearts in the pack. Finally, we will use the formula for probability to get the required probability.
Formula Used: We will use the formula of the probability of an event is given by \[P\left( E \right) = \] Number of favourable outcomes \[ \div \] Number of total outcomes.

Complete step by step solution:
First, we will find the number of favourable outcomes and total outcomes.
The total number of cards in the pack is 52.
Therefore, the total number of possible outcomes when a card is picked from the pack is 52.
Next, we will find the number of favourable outcomes.
There are 4 queens (1 each of clubs, spades, diamonds, hearts) in a pack.
Thus, there is only 1 queen of clubs in a pack of 52 cards.
Similarly, there are 4 kings (1 each of clubs, spades, diamonds, hearts) in a pack.
Thus, there is only 1 king of hearts in a pack of 52 cards.
We need the probability of getting either a king of hearts, or a queen of clubs when 1 card is drawn from a pack of 52 cards
Therefore, the number of favourable outcomes is 2.
Finally, we will use the formula for probability of an event to calculate the probability of getting a card of diamond.
Let \[E\] be the event of getting a queen of clubs or a king of hearts.
Substituting 2 for the number of favourable outcomes, and 52 for the number of total outcomes in the formula, we get
\[ \Rightarrow P\left( E \right) = \dfrac{2}{{52}}\]
The numerator 2 and the denominator 52 are both divisible by 2.
Simplifying the expression, we get
\[ \Rightarrow P\left( E \right) = \dfrac{1}{{26}}\]
Therefore, the probability of getting a queen of clubs or a king of hearts when one card is drawn from a pack of 52 cards is \[\dfrac{1}{{26}}\].

Thus, the correct option is option (c).

Note:
We calculated the probability of getting a queen of clubs or a king of hearts when one card is drawn from a pack of 52 cards. The probability of an event is the chance of that event occurring. It always lies between 0 and 1, both inclusive. The probability of an event can never be negative or greater than 1.