Question

From a well shuffled pack of 52 cards, one card drawn at random. Find the probability of getting a heart.

Answer 1

Hint: Heart is one type of suit in a pack of cards and there are a total 4 suits in the pack of cards. So there are 13 heart cards in a pack of 52 cards (divide 52 by 4 so we will get 13).

Complete step by step solution:
Total cards in a pack is equal to \[52\]
Total number of hearts in a pack of \[52\]cards is\[13\].
Let the probability of getting a heart be P(H)
$\Rightarrow \operatorname{P}(H)=\dfrac{Number\,of\,heart\,cards\,in\,a\,pack\,of\,card}{Total\,number\,of\,cards}$
$\Rightarrow \operatorname{P}(H)=\dfrac{13}{52}=\dfrac{1}{4}$
So, the probability of getting a heart is \[\dfrac{1}{4}\]

Note: 1) I we will use the formula-
\[\text{probability = }\dfrac{\text{No}\text{. of favourable outcomes}}{\text{Total outcomes}}\]
To find the probability of all (diamonds, hearts, spades and clubs)
2) The number of cards of each of these type is \[\text{13}\]
3) The probability should always be reduced to lowest form
For ex \[\dfrac{13}{52}=\dfrac{1}{4}\]