Solution: We use the basic formula of probability to solve the problem. Probability = Number of possible outcomes/Total number of favorable outcomes. Total number of cards from a well-shuffled deck = 52 Number of spade cards = 13 Number of heart cards = 13 Number of diamond cards = 13 Number of club cards = 13 Total number of kings = 4 Total number of queens = 4 Total number of jacks = 4 Number of face cards = 12 (i) Probability of getting a king of red colour = Number of red colour king/Total number of outcomes We will have 2 red kings (Heart and Diamond) = 2/52 = 1/26 (ii) Probability of getting a face card = Number of face cards/Total number of outcomes 12/52 = 3/13 (iii) Probability of getting a red face card = Number of red face cards/Total number of outcomes We will have 3 diamond face cards and 3 heart face cards that sum up to 6 red face cards. = 6/52 = 3/26 (iv) Probability of getting the jack of hearts = Number of jack of hearts/Total number of outcomes = 1/52 (v) Probability of getting a spade card = Number of spade cards/Total number of outcomes = 13/52 = 1/4 (vi) Probability of getting the queen of diamonds = Number of possible outcomes/Total number of favourable outcomes = 1/52 Check out more in terms of probability. β Check: NCERT Solutions for Class 10 Maths Chapter 15 Video Solution: NCERT Solutions for Class 10 Maths Chapter 15 Exercise 15.1 Question 14 Summary: If one card is drawn from a well-shuffled deck of 52 cards, then the probability of getting (i) a king of red colour, (ii) a face card, (iii) a red face card, (iv) the jack of hearts, (v) a spade, and (vi) the queen of diamonds are 1/26, 3/13, 3/26, 1/52, 1/4, and 1/52 respectively. β Related Questions:
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Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that card will be a diamond Since there 52 cards n(S) = Total number of cards = 52 There are 13 diamond cards Let A be event that diamond card is withdrawn So, n(A) = 13 Probability of A = P(A) = (ππ’ππππ ππ πππππππ πππππ )/(πππ‘ππ ππ’ππππ ππ πππππ ) = (n(A))/(n(S)) = 13/52 = π/π Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that card will be (ii) not an ace There are 4 ace cards Let B be the event that card drawn is ace So, n(B) = 4 Hence Probability card drawn is ace = P(B) = (ππ’ππππ ππ πππ πππππ )/(πππ‘ππ ππ’ππππ ππ πππππ ) = (n(A))/(n(S)) = 4/52 = 1/13 Probability that card is not an ace = P(Bβ) = 1 β P(B) = 1 β 1/13 = (13 β 1)/13 = ππ/ππ Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that card will be (iii) a black card (i.e., a club or, a spade) There are 26 black cards (13 spade and 13 club) Let C be the probability that card drawn is black n(C) = 13 + 13 = 26 Hence Probability card drawn is black = P(C) = (ππ’ππππ ππ πππππ πππππ )/(πππ‘ππ ππ’ππππ ππ πππππ ) = (n(C))/(n(S)) = 26/52 = π/π Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that card will be (iv) not a diamond From part (i) , A is the event that card is diamond So, Aβ is event that card is not diamond Probability card is not a diamond = P(Aβ) = 1 β P(A) = 1 β 1/4 = (4 β 1)/4 = π/π Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that card will be (v) not a black card From part (iii) , C is the event that card is black So, Cβ is event that card is not black Probability card is not a black = P(Cβ) = 1 β P(C) = 1 β 1/2 = π/π Page 2
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Example, 11 A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be (i) red, There are 9 discs of which 4 are red 3 are blue & 2 are yellow Total number of possible outcomes is 9 n(S) = 9 Let A be the event that the disc is red B be the event that the disc is yellow C be the event that the disc is blue Red Number of red discs = 4 i.e. n(A) = 4 Probability of drawing red discs = P(A) = n(A) n(S) = Example, 11 A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag.Calculate the probability that it will be (ii) yellow, Number of yellow disc = 2 i.e. n(B) = 2 Probability of drawing yellow disc = P(B) = n(B) n(S) = Example, 11 A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be (iii) blue, Number of blue disc = 3 i.e. n(C) = 3 Probability of drawing blue disc = P(C) = n(C) n(S) = 3 9 = Example, 11 A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be (iv) not blue, P(not blue) = 1 P(blue) = 1 P(C) = 1 1 3 = 3 1 3 = Example, 11 A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be (v) either Red or Blue, Either red or blue describes the set (A or B) Since we can take either red disc or blue, There is nothing is common in A & B A or B are mutually exclusive Hence A B = So, P(A B) = 0 We need to find P(A B) We know that P(A B) = P(A) + P(B) P(A B) Putting values P(A B) = 4 9 + 1 3 0 = 4 + 3 9 = 7 9 Hence, P(A B) = Hence probability of either red or blue is 7 9 |
One card is drawn from a well-shuffled deck of 52 cards then which of the following is true
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