Question

How do you find the probability of picking a diamond from a standard deck of cards which has 13 cards in each of four suits: spades, hearts, diamonds, and clubs, in a simplified fraction?

Answer 1

Hint: To obtain the probability of picking a diamond from a standard deck of cards use the information given. First count the total number of possible outcomes then find the total number of favorable outcomes for the card to be from a diamond suit. Finally divide the number of possible outcomes by favorable outcome for the card to be from a diamond suit.

Complete step-by-step solution:
It is given that there are 13 cards of each suit and the number of suits are four which are spades, hearts, diamonds, and clubs.
So total number of possible outcome $=13\times 4$
$n\left( S \right)=52$…..$\left( 1 \right)$
Now, the favorable outcome is number of card in a diamond suit so:
$n\left( E \right)=13$…..$\left( 2 \right)$
Probability formula is given as:
$P\left( E \right)=\dfrac{n\left( E \right)}{n\left( S \right)}$
Substituting the value from equation (1) and (2) in above formula we get,
\[\begin{align}
  & P\left( E \right)=\dfrac{13}{52} \\
 & \Rightarrow P\left( E \right)=\dfrac{1}{4} \\
\end{align}\]
$\therefore P\left( E \right)=\dfrac{1}{4}$
Hence probability of picking a diamond from a standard deck of cards is $\dfrac{1}{4}$

Note: Probability is that branch of mathematics which deals with the information of how likely an event is to occur. Always check that your answer is between 0 and 1 as the probability of an event can never be negative. If the probability is 0 that means the event is impossible to occur and if probability is 1 the event will definitely occur. The probability can take any value between 0 and 1 for example- If we toss a coin the probability of coming Head is half as there are only two outcomes of this a Head or a Tail .