Question

How do you find the probability of selecting a red face card from a standard deck of playing cards?

Answer 1

Hint: Here in this question, we have to find the probability of number of chances to select the red face card from a pack of 52 playing cards, for this first we have to find out the how many red face cards are their later as by the definition of probability i.e., the ratio of the number of favourable outcomes and the total number of outcomes. On simplification we get the required solution.

Complete step by step solution:
Probability is a Method to study in Mathematics which deals with the possibility of occurrence or non-occurrence of a given event out of the Entire occurrences that can happen in the given situation or Condition.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
The probability of an event, represented by \[P\left( E \right)\] is given by
\[P\left( E \right) = \dfrac{{\text{Number of favourable outcomes}}}{{\text{Total Number of outcomes}}}\]
Another Thing to Know for the question is about Cards.
A deck of playing cards consists of 52 cards. This deck is divided into 4 different suits, having 13 cards each. The 4 decks are having designs on them named as Hearts, Diamonds, Spades and Clubs. The Hearts and Diamonds are Red coloured & Spades and Clubs are Black coloured. Each of the Above Suits Contains a King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2 and an Ace. But King, Queen and Jack are Recognized as Face Cards.
We need to find out the probability of getting a red face card from a well shuffled deck of 52 cards: so in this case,
Total Number of Face cards in a deck will be \[3 \times 4 = 12\] Face Cards.
Out of the 12 Face cards, 6 are Black and 6 are Red.
So, Favourable Outcomes = Number of Red Face Cards = 6
And Total Outcomes = Total Number of cards in a deck = 52
So, Probability of getting a red face card from deck of 52 cards: i.e.
\[P\left( E \right) = \dfrac{{\text{Number of favourable outcomes}}}{{\text{Total Number of outcomes}}}\]
\[ \Rightarrow \,P(E) = \dfrac{6}{{52}}\]
Or
\[ \Rightarrow \,P(E) = \dfrac{3}{{26}}\]
It’s a required solution.
So, the correct answer is “$\dfrac{3}{{26}}$”.

Note: To Find the Probability of an Event, you merely need to Find the Favourable and Total outcome. The difficulty in these sorts of questions is finding the Favourable Outcomes in a complex situation, first we have to know about the playing cards i.e., know the types of cards, colours etc.