Question

The probability of drawing a red 9 from a standard pack of 52 playing cards is
A. \[\dfrac{1}{{13}}\]
B. \[\dfrac{1}{{26}}\]
C. \[\dfrac{1}{2}\]
D. \[\dfrac{1}{4}\]

Answer 1

Hint: We need to determine the probability of card number 9 which is to be of red color from the pack of 52 cards. So, as we know that there are a total of 26 cards of each color in a deck of 52 cards and only 2 numbers are present in each color thus, we can have the number of favorable outcomes from this information and dividing by total outcomes will give us the required probability.

Complete step by step solution:
First, we will consider the data given that is a deck of 52 cards and we need to find the number 9 of red color present in the deck.
In other words we can say that we have to find the probability of drawing a card from a standard pack of 52 playing cards which is red in color and has 9 written on it.

We know that there are 4 suits of 13 cards each in a deck of 52 playing cards. Out of these 4 suits, 2 suits have red cards and 2 suits have black cards. We also know that each suit contains 1 King, 1 Queen, 1 Jack, 1 Ace and one card each of 10, 9, 8, 7, 6, 5, 4, 3 and 2.

That means there are a total 26 red cards and out of these 26 red cards 2 red cards are of 9. We know that the total number of possible outcomes is 52.
Number of favorable outcomes that is red 9 is 2.
Therefore, probability of getting a red 9 is as follows:
\[
   \Rightarrow P = \dfrac{{{\text{Number of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}} \\
   \Rightarrow P = \dfrac{2}{{52}} \\
   \Rightarrow P = \dfrac{1}{{26}} \\
 \]
Thus, we get the probability of getting a red color card written 9 on it is \[\dfrac{1}{{26}}\]
Therefore, the correct option is B.

Note: In this question, first of all, note that the total number of possible outcomes is 52. A standard pack 52 cards are equally divided into 4 suits which are spades, hearts, diamonds, and clubs. But in this question, we do not have to divide the pack in these four suits. We will only consider a number of cards of 9 in red color for favorable outcomes.