Question

Find the probability of getting a red card from a well shuffled pack of cards.

Answer 1

Hint: Half of the number of cards are red and half are black in the pack of cards. Use the definition of the probability. Probability of any event is the ratio of the favourable outcomes to the total outcomes.

Complete step-by-step answer:
We are given a well shuffled pack of cards.
We have to find the probability of getting a red card from a well shuffled pack of cards.
First, we understand about $52$ cards.
$52$ cards are divided equally among black and red colours. It means $26$ cards are black colour and cards are red colour$26$
Now, we define how we evaluate the probability of our event.
Probability of any event A is the ratio of favourable outcomes for that event to the total outcomes.
The formula for the probability is defined as:
\[P(A) = \dfrac{{Favourable\,outcomes}}{{Total\,outcomes}}\]
Since, there are $26$ cards are red therefore, favourable outcomes will be $26$.
Total outcomes in the well shuffled pack of cards is $52$.
Therefore, probability of getting a red card from a well shuffled pack of cards is
$
P = \dfrac{{26}}{{52}} \\
\Rightarrow P = \dfrac{1}{2} \\
 $
 Hence, the probability of getting a red card is .
\[\dfrac{1}{2}\]
Additional Information:
There are $4$ types of cards namely Spade, Diamond, Club and Heart. The colour of spade and club cards are black where the colour of diamond and heart cards are red.
In each type of card there are $3$ face cards namely King, Queen and Jack. It means there are $4$ kings, $4$ queens and $4$ jacks in a pack of $52$ cards.
There is one Ace in each type of card. It means there are $4$ Aces in a pack of $52$ cards.
Rest of the cards are numbered from $2$ to $10$ in each type.

Note:
For two equal events, the probability of both the events is $\dfrac{1}{2}$. So, we can directly write the probability of red cards as $\dfrac{1}{2}$ because $52$ cards are divided equally among black and red colours.