Question

The king, queen and jack of hearts are removed from a deck of $52$ playing cards and well shuffled. One card is selected from the remaining cards. The probability of drawing a $10$ of hearts is
A.$\dfrac{{10}}{{49}}$
B.$\dfrac{{13}}{{49}}$
C.$\dfrac{3}{{49}}$
D.$\dfrac{1}{{49}}$

Answer 1

Hint - To solve this problem, firstly one should know about the term probability and the concept behind a deck of cards. So, we will be learning the concept behind a deck of cards and combining it with the concept of probability, we will be approaching our answer.

Complete step-by-step answer:
There are a total of $52$ cards in a deck. There are $13$ ranks of cards. These ranks include the numbers $2\,to10$ , jack, queen, king, and ace. There are four suits: Hearts, diamonds, spades and clubs .Thus there are $13$ hearts, $13$diamonds, $13$spades and $13$clubs. The jacks, queen and king are all considered face cards .$\therefore $ , three face cards for each suit and a total of $12$ face cards in the deck.
King, queen and jack are known as face cards so total face cards=$12$
After removing the King, queen and Jack of clubs from a deck of $52$ cards,
Number of Total cards left $ = 52 - 3 = 49$
Number of club card left$ = 13 - 3 = 10$
Number of heart cards$ = 13$
Now, what is Probability -
In simple words, Probability means how likely something is going to happen, or the chances of something to happen.
Now let’s come to our question.
So, the probability of getting a heart$ = \dfrac{{13}}{{49}}$
The probability of getting a club$ = \dfrac{{10}}{{49}}$
The probability of getting the $10$ of hearts$ = \dfrac{1}{{49}}$ (as there is only $1$ card of $10$(hearts))
So, the correct answer is option D - $\dfrac{1}{{49}}$

Note - A deck of playing cards consists of $52$ cards out of which $26$ are black cards and other $26$ are red cards. Whereas red cards consist of $13$ cards of heart, $13$ cards of diamond and black cards of $13$ cards of spades and $13$ cards of clubs.