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Important Notes
The suits which are represented by red cards are hearts and diamonds while the suits represented by black cards are spades and clubs. There are 26 red cards and 26 black cards. Let's learn about the suits in a deck of cards. Suits in a deck of cards are the representations of red and black color on the cards. Based on suits, the types of cards in a deck are: There are 52 cards in a deck. Each card can be categorized into 4 suits constituting 13 cards each. These cards are also known as court cards. They are Kings, Queens, and Jacks in all 4 suits. All the cards from 2 to 10 in any suit are called the number cards. These cards have numbers on them along with each suit being equal to the number on number cards. There are 4 Aces in every deck, 1 of every suit.
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Now that you know all about facts about a deck of cards, you can draw a card from a deck and find its probability easily. How to Determine the Probability of Drawing a Card?Let's learn how to find probability first. Now you know that probability is the ratio of number of favorable outcomes to the number of total outcomes, let's apply it here. ExamplesExample 1: What is the probability of drawing a king from a deck of cards? Solution: Here the event E is drawing a king from a deck of cards. There are 52 cards in a deck of cards. Hence, total number of outcomes = 52 The number of favorable outcomes = 4 (as there are 4 kings in a deck) Hence, the probability of this event occuring is P(E) = 4/52 = 1/13
Example 2: What is the probability of drawing a black card from a pack of cards? Solution: Here the event E is drawing a black card from a pack of cards. The total number of outcomes = 52 The number of favorable outcomes = 26 Hence, the probability of event occuring is P(E) = 26/52 = 1/2
Solved ExamplesJessica has drawn a card from a well-shuffled deck. Help her find the probability of the card either being red or a King. Solution Jessica knows here that event E is the card drawn being either red or a King. The total number of outcomes = 52 There are 26 red cards, and 4 cards which are Kings. However, 2 of the red cards are Kings. If we add 26 and 4, we will be counting these two cards twice. Thus, the correct number of outcomes which are favorable to E is 26 + 4 - 2 = 28 Hence, the probability of event occuring is P(E) = 28/52 = 7/13
Help Diane determine the probability of the following:
Solution Diane knows here the events E1, E2, and E3 are Drawing a Red Queen, Drawing a King of Spades, and Drawing a Red Number Card. The total number of outcomes in every case = 52 There are 26 red cards, of which 2 are Queens. Hence, the probability of event E1 occuring is P(E1) = 2/52 = 1/26 There are 13 cards in each suit, of which 1 is King. Hence, the probability of event E2 occuring is P(E2) = 1/52
There are 9 number cards in each suit and there are 2 suits which are red in color. There are 18 red number cards. Hence, the probability of event E3 occuring is P(E3) = 18/52 = 9/26
Interactive QuestionsHere are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result. We hope you enjoyed learning about probability of drawing a card from a pack of 52 cards with the practice questions. Now you will easily be able to solve problems on number of cards in a deck, face cards in a deck, 52 card deck, spades hearts diamonds clubs in pack of cards. Now you can draw a card from a deck and find its probability easily . The mini-lesson targeted the fascinating concept of card probability. The math journey around card probability starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that is not only relatable and easy to grasp, but will also stay with them forever. Here lies the magic with Cuemath. About CuemathAt Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students! Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic. Be it problems, online classes, videos, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.
We find the ratio of the favorable outcomes as per the condition of drawing the card to the total number of outcomes, i.e, 52. 2. What is the probability of drawing any face card?Probability of drawing any face card is 6/26. 3. What is the probability of drawing a red card?Probability of drawing a red card is 1/2. 4. What is the probability of drawing a king or a red card?Probability of drawing a king or a red card is 7/13. 5. What is the probability of drawing a king or a queen?The probability of drawing a king or a queen is 2/13. 6. What are the 5 rules of probability?The 5 rules of probability are: For any event E, the probability of occurence of E will always lie between 0 and 1 The sum of probabilities of every possible outcome will always be 1 The sum of probability of occurence of E and probability of E not occuring will always be 1 When any two events are not disjoint, the probability of occurence of A and B is not 0 while when two events are disjoint, the probability of occurence of A and B is 0. As per this rule, P(A or B) = (P(A) + P(B) - P(A and B)). 7. What is the probability of drawing a king of hearts?Probability of drawing a king of hearts is 1/52. 8. Is Ace a face card in probability?No, Ace is not a face card in probability. 9. What is the probability it is not a face card?The probability it is not a face card is 10/13. 10. How many black non-face cards are there in a deck?There are 20 black non-face cards in a deck.
Learning Outcomes
Probability is the likelihood of a particular outcome or event happening. Statisticians and actuaries use probability to make predictions about events. An actuary that works for a car insurance company would, for example, be interested in how likely a 17 year old male would be to get in a car accident. They would use data from past events to make predictions about future events using the characteristics of probabilities, then use this information to calculate an insurance rate. In this section, we will explore the definition of an event, and learn how to calculate the probability of it’s occurance. We will also practice using standard mathematical notation to calculate and describe different kinds of probabilities. Basic ConceptsIf you roll a die, pick a card from deck of playing cards, or randomly select a person and observe their hair color, we are executing an experiment or procedure. In probability, we look at the likelihood of different outcomes. We begin with some terminology. Events and Outcomes
If we roll a standard 6-sided die, describe the sample space and some simple events.
Given that all outcomes are equally likely, we can compute the probability of an event E using this formula: [latex]P(E)=\frac{\text{Number of outcomes corresponding to the event E}}{\text{Total number of equally-likely outcomes}}[/latex]
If we roll a 6-sided die, calculate
This video describes this example and the previous one in detail. Let’s say you have a bag with 20 cherries, 14 sweet and 6 sour. If you pick a cherry at random, what is the probability that it will be sweet?
At some random moment, you look at your clock and note the minutes reading. a. What is probability the minutes reading is 15? b. What is the probability the minutes reading is 15 or less?
A standard deck of 52 playing cards consists of four suits (hearts, spades, diamonds and clubs). Spades and clubs are black while hearts and diamonds are red. Each suit contains 13 cards, each of a different rank: an Ace (which in many games functions as both a low card and a high card), cards numbered 2 through 10, a Jack, a Queen and a King.
Compute the probability of randomly drawing one card from a deck and getting an Ace. This video demonstrates both this example and the previous cherry example on the page. Certain and Impossible events
In the course of this section, if you compute a probability and get an answer that is negative or greater than 1, you have made a mistake and should check your work. Types of EventsComplementary EventsNow let us examine the probability that an event does not happen. As in the previous section, consider the situation of rolling a six-sided die and first compute the probability of rolling a six: the answer is P(six) =1/6. Now consider the probability that we do not roll a six: there are 5 outcomes that are not a six, so the answer is P(not a six) = [latex]\frac{5}{6}[/latex]. Notice that [latex]P(\text{six})+P(\text{not a six})=\frac{1}{6}+\frac{5}{6}=\frac{6}{6}=1[/latex] This is not a coincidence. Consider a generic situation with n possible outcomes and an event E that corresponds to m of these outcomes. Then the remaining n – m outcomes correspond to E not happening, thus [latex]P(\text{not}E)=\frac{n-m}{n}=\frac{n}{n}-\frac{m}{n}=1-\frac{m}{n}=1-P(E)[/latex]
The complement of an event is the event “E doesn’t happen”
If you pull a random card from a deck of playing cards, what is the probability it is not a heart? This situation is explained in the following video. Probability of two independent events
Suppose we flipped a coin and rolled a die, and wanted to know the probability of getting a head on the coin and a 6 on the die. The prior example contained two independent events. Getting a certain outcome from rolling a die had no influence on the outcome from flipping the coin.
Events A and B are independent events if the probability of Event B occurring is the same whether or not Event A occurs.
Are these events independent?
When two events are independent, the probability of both occurring is the product of the probabilities of the individual events.
If events A and B are independent, then the probability of both A and B occurring is [latex]P\left(A\text{ and }B\right)=P\left(A\right)\cdot{P}\left(B\right)[/latex] where P(A and B) is the probability of events A and B both occurring, P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring If you look back at the coin and die example from earlier, you can see how the number of outcomes of the first event multiplied by the number of outcomes in the second event multiplied to equal the total number of possible outcomes in the combined event.
In your drawer you have 10 pairs of socks, 6 of which are white, and 7 tee shirts, 3 of which are white. If you randomly reach in and pull out a pair of socks and a tee shirt, what is the probability both are white? Examples of joint probabilities are discussed in this video. The previous examples looked at the probability of both events occurring. Now we will look at the probability of either event occurring.
Suppose we flipped a coin and rolled a die, and wanted to know the probability of getting a head on the coin or a 6 on the die.
The probability of either A or B occurring (or both) is [latex]P(A\text{ or }B)=P(A)+P(B)–P(A\text{ and }B)[/latex]
Suppose we draw one card from a standard deck. What is the probability that we get a Queen or a King? See more about this example and the previous one in the following video. In the last example, the events were mutually exclusive, so P(A or B) = P(A) + P(B).
Suppose we draw one card from a standard deck. What is the probability that we get a red card or a King?
In your drawer you have 10 pairs of socks, 6 of which are white, and 7 tee shirts, 3 of which are white. If you reach in and randomly grab a pair of socks and a tee shirt, what the probability at least one is white?
The table below shows the number of survey subjects who have received and not received a speeding ticket in the last year, and the color of their car. Find the probability that a randomly chosen person:
This table example is detailed in the following explanatory video. Conditional ProbabilityIn the previous section we computed the probabilities of events that were independent of each other. We saw that getting a certain outcome from rolling a die had no influence on the outcome from flipping a coin, even though we were computing a probability based on doing them at the same time. In this section, we will consider events that are dependent on each other, called conditional probabilities.
The probability the event B occurs, given that event A has happened, is represented as P(B | A) This is read as “the probability of B given A” For example, if you draw a card from a deck, then the sample space for the next card drawn has changed, because you are now working with a deck of 51 cards. In the following example we will show you how the computations for events like this are different from the computations we did in the last section.
What is the probability that two cards drawn at random from a deck of playing cards will both be aces?
If Events A and B are not independent, then P(A and B) = P(A) · P(B | A)
If you pull 2 cards out of a deck, what is the probability that both are spades?
The table below shows the number of survey subjects who have received and not received a speeding ticket in the last year, and the color of their car. Find the probability that a randomly chosen person:
These kinds of conditional probabilities are what insurance companies use to determine your insurance rates. They look at the conditional probability of you having accident, given your age, your car, your car color, your driving history, etc., and price your policy based on that likelihood. View more about conditional probability in the following video.
If you draw two cards from a deck, what is the probability that you will get the Ace of Diamonds and a black card? These two playing card scenarios are discussed further in the following video.
A home pregnancy test was given to women, then pregnancy was verified through blood tests. The following table shows the home pregnancy test results. Find
See more about this example here. |
What is the probability that a card drawn at random from a standard deck of cards will be a Jack what type of probability concept did you apply in this case?
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