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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 wellshuffled 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 minilesson 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 learningteachinglearning 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 nonface cards are there in a deck?There are 20 black nonface cards in a deck.
Playing cards probability problems based on a wellshuffled deck of 52 cards. Basic concept on drawing a card: In a pack or deck of 52 playing cards, they are divided into 4 suits of 13 cards each i.e. spades ♠ hearts ♥, diamonds ♦, clubs ♣. Cards of Spades and clubs are black cards. Cards of hearts and diamonds are red cards. The card in each suit, are ace, king, queen, jack or knaves, 10, 9, 8, 7, 6, 5, 4, 3 and 2. King, Queen and Jack (or Knaves) are face cards. So, there are 12 face cards in the deck of 52 playing cards. Workedout problems on Playing cards probability: 1. A card is drawn from a well shuffled pack of 52 cards. Find the probability of: (i) ‘2’ of spades (ii) a jack (iii) a king of red colour (iv) a card of diamond (v) a king or a queen (vi) a nonface card (vii) a black face card (viii) a black card (ix) a nonace (x) nonface card of black colour (xi) neither a spade nor a jack (xii) neither a heart nor a red king Solution: In a playing card there are 52 cards. Therefore the total number of possible outcomes = 52 (i) ‘2’ of spades: Number of favourable outcomes i.e. ‘2’ of spades is 1 out of 52 cards. Therefore, probability of getting ‘2’ of spade Number of favorable outcomesP(A) = Total number of possible outcome = 1/52 (ii) a jack Number of favourable outcomes i.e. ‘a jack’ is 4 out of 52 cards. Therefore, probability of getting ‘a jack’ Number of favorable outcomesP(B) = Total number of possible outcome = 4/52 = 1/13 (iii) a king of red colour Number of favourable outcomes i.e. ‘a king of red colour’ is 2 out of 52 cards. Therefore, probability of getting ‘a king of red colour’ Number of favorable outcomesP(C) = Total number of possible outcome = 2/52 = 1/26 (iv) a card of diamond Number of favourable outcomes i.e. ‘a card of diamond’ is 13 out of 52 cards. Therefore, probability of getting ‘a card of diamond’ Number of favorable outcomesP(D) = Total number of possible outcome = 13/52 = 1/4 (v) a king or a queen Total number of king is 4 out of 52 cards. Total number of queen is 4 out of 52 cards Number of favourable outcomes i.e. ‘a king or a queen’ is 4 + 4 = 8 out of 52 cards. Therefore, probability of getting ‘a king or a queen’ Number of favorable outcomesP(E) = Total number of possible outcome = 8/52 = 2/13 (vi) a nonface card Total number of face card out of 52 cards = 3 times 4 = 12 Total number of nonface card out of 52 cards = 52  12 = 40 Therefore, probability of getting ‘a nonface card’ Number of favorable outcomesP(F) = Total number of possible outcome = 40/52 = 10/13 (vii) a black face card: Cards of Spades and Clubs are black cards. Number of face card in spades (king, queen and jack or knaves) = 3 Number of face card in clubs (king, queen and jack or knaves) = 3 Therefore, total number of black face card out of 52 cards = 3 + 3 = 6 Therefore, probability of getting ‘a black face card’ Number of favorable outcomesP(G) = Total number of possible outcome = 6/52 = 3/26 (viii) a black card: Cards of spades and clubs are black cards. Number of spades = 13 Number of clubs = 13 Therefore, total number of black card out of 52 cards = 13 + 13 = 26 Therefore, probability of getting ‘a black card’ Number of favorable outcomesP(H) = Total number of possible outcome = 26/52 = 1/2 (ix) a nonace: Number of ace cards in each of four suits namely spades, hearts, diamonds and clubs = 1 Therefore, total number of ace cards out of 52 cards = 4 Thus, total number of nonace cards out of 52 cards = 52  4 = 48 Therefore, probability of getting ‘a nonace’ Number of favorable outcomesP(I) = Total number of possible outcome = 48/52 = 12/13 (x) nonface card of black colour: Cards of spades and clubs are black cards. Number of spades = 13 Number of clubs = 13 Therefore, total number of black card out of 52 cards = 13 + 13 = 26 Number of face cards in each suits namely spades and clubs = 3 + 3 = 6 Therefore, total number of nonface card of black colour out of 52 cards = 26  6 = 20 Therefore, probability of getting ‘nonface card of black colour’ P(J) = Total number of possible outcome = 20/52 = 5/13 (xi) neither a spade nor a jack Number of spades = 13 Total number of nonspades out of 52 cards = 52  13 = 39 Number of jack out of 52 cards = 4 Number of jack in each of three suits namely hearts, diamonds and clubs = 3 [Since, 1 jack is already included in the 13 spades so, here we will take number of jacks is 3] Neither a spade nor a jack = 39  3 = 36 Therefore, probability of getting ‘neither a spade nor a jack’ Number of favorable outcomesP(K) = Total number of possible outcome = 36/52 = 9/13 (xii) neither a heart nor a red king Number of hearts = 13 Total number of nonhearts out of 52 cards = 52  13 = 39 Therefore, spades, clubs and diamonds are the 39 cards. Cards of hearts and diamonds are red cards. Number of red kings in red cards = 2 Therefore, neither a heart nor a red king = 39  1 = 38 [Since, 1 red king is already included in the 13 hearts so, here we will take number of red kings is 1] Therefore, probability of getting ‘neither a heart nor a red king’ Number of favorable outcomesP(L) = Total number of possible outcome = 38/52 = 19/26 2. A card is drawn at random from a wellshuffled pack of cards numbered 1 to 20. Find the probability of (i) getting a number less than 7 (ii) getting a number divisible by 3. Solution: (i) Total number of possible outcomes = 20 ( since there are cards numbered 1, 2, 3, ..., 20). Number of favourable outcomes for the event E = number of cards showing less than 7 = 6 (namely 1, 2, 3, 4, 5, 6). So, P(E) = \(\frac{\textrm{Number of Favourable Outcomes for the Event E}}{\textrm{Total Number of Possible Outcomes}}\) = \(\frac{6}{20}\) = \(\frac{3}{10}\). (ii) Total number of possible outcomes = 20. Number of favourable outcomes for the event F = number of cards showing a number divisible by 3 = 6 (namely 3, 6, 9, 12, 15, 18). So, P(F) = \(\frac{\textrm{Number of Favourable Outcomes for the Event F}}{\textrm{Total Number of Possible Outcomes}}\) = \(\frac{6}{20}\) = \(\frac{3}{10}\). 3. A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is (i) a king (ii) neither a queen nor a jack. Solution: Total number of possible outcomes = 52 (As there are 52 different cards). (i) Number of favourable outcomes for the event E = number of kings in the pack = 4. So, by definition, P(E) = \(\frac{4}{52}\) = \(\frac{1}{13}\). (ii) Number of favourable outcomes for the event F = number of cards which are neither a queen nor a jack = 52  4  4, [Since there are 4 queens and 4 jacks]. = 44 Therefore, by definition, P(F) = \(\frac{44}{52}\) = \(\frac{11}{13}\). These are the basic problems on probability with playing cards.
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