Kaliyuga Ekalavya

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 25 Question: Which of the following arguments are correct and which are not correct? Give reasons for your answer. (i) If two coins are tossed simultaneously there are three possible outcomes —two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1 3 (ii) If a die is thrown, there are two possible outcomes— an odd number or an even number. Therefore, the probability of getting an odd number is 1 2 Given: (i) Two coins are tossed simultaneously. (ii) A die is thrown. To Find: Whether the given arguments are correct or not, with reasons. Formula: Probability = Number of favorable outcomes Total number of possible outcomes Solution: (i) When two coins are tossed simultaneously,  the possible outcomes are: HH, HT, TH, TT.  There are 4 possible outcomes, not 3.  The argument that there are only three outcomes (two heads, two tails, or one of eac...

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 21 Question: A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that (i) She will buy it ? (ii) She will not buy it ? Given: Total number of ball pens = 144 Number of defective pens = 20 Number of good pens = 144 - 20 = 124 To Find: (i) Probability that Nuri will buy the pen (ii) Probability that Nuri will not buy the pen Formula: Probability = Number of favorable outcomes Total number of outcomes Solution: (i) Probability that Nuri will buy the pen (i.e., the pen is good) ⇒ Probability = 124 144 = 31 36 (ii) Probability that Nuri will not buy the pen (i.e., the pen is defective) ⇒ Probability = 20 144 = 5 36 Result: (i) The probability that she will buy the pe...

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 24 Question: A die is thrown twice. What is the probability that (i) 5 will not come up either time? (ii) 5 will come up at least once? Given: A die is thrown twice. To Find: (i) Probability that 5 will not come up either time. (ii) Probability that 5 will come up at least once. Formula: Probability = Favorable Outcomes Total Outcomes Solution: (i) Probability that 5 will not come up either time: Total outcomes = 6 × 6 = 36 Outcomes where 5 does not come up = 5 × 5 = 25 Probability = 25 36 (ii) Probability that 5 will come up at least once: This can be calculated as 1 - P(5 does not come up either time) Probability = 1 - 25 36 = 11 36 Result: (i) Probability that 5 will not come up either time = 25 36 (ii) Probability that 5 will come up at least once = 11 36 Next question solution: NCERT Class X Chapter 14: Probability Exercis...

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 23 Question: A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game. Given: A coin is tossed 3 times. Hanif wins if all tosses are heads or all are tails. He loses otherwise. To Find: The probability that Hanif will lose the game. Formula: Probability = Favorable Outcomes Total Outcomes Solution: Total possible outcomes when a coin is tossed 3 times = 2 3 = 8 Outcomes where Hanif wins (all heads or all tails) = 2 Outcomes where Hanif loses = Total outcomes - Outcomes where Hanif wins = 8 - 2 = 6 Probability that Hanif will lose = 6 8 = 3 4 Result: The probability that Hanif will lose the game is 3 4 . Next question solution: NCERT Class X Chapter 14: Probabi...

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 22 Question: Refer to Example 13. Example 13: Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. (i) Complete the following table: Event: 'Sum on 2 dice' 2 3 4 5 6 7 8 9 10 11 12 Probability \(\frac{1}{36}\) \(\frac{5}{36}\) \(\frac{1}{36}\) (ii) A student argues that “there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability \(\frac{1}{11}\).” Do you agree with this argument? Justify your answer. Given: Two dice are thrown simultaneously. Each die has 6 faces numbered 1 to 6. Therefore, the total number of possible outcomes = 36. To Find: 1. The probability of each possible sum on two dice. 2. Whether the student's argument that each sum has probability \(\frac{1}{11}\) is correct. Formula: Probability of an event = $$ P(E) = \frac{\text{Number of f...

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 19 Question: A child has a die whose six faces show the letters as given below: A B C D E A. The die is thrown once. What is the probability of getting (i) A? (ii) D? Given: A die with faces showing the letters: A, B, C, D, E, A. The die is thrown once. To Find: (i) Probability of getting A (ii) Probability of getting D Formula: Probability = Number of favorable outcomes Total number of possible outcomes Solution: (i) Probability of getting A: Number of favorable outcomes (A) = 2 Total number of possible outcomes = 6 Probability (A) = 2 6 = 1 3 (ii) Probability of getting D: Number of favorable outcomes (D) = 1 Total number of possible outcomes = 6 Probability (D) = 1 6 Result: (i) Probability of getting A = 1 3 (ii) Probability of getting D = 1 6 Next question solution: NCERT Class X Chapter 14: Probability Exercise 14.1 Question 21 ...

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 18 Question: A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5. Given: Total number of discs = 90. Discs are numbered from 1 to 90. To Find: (i) Probability of drawing a two-digit number. (ii) Probability of drawing a perfect square number. (iii) Probability of drawing a number divisible by 5. Formula: Probability = Number of favorable outcomes Total number of outcomes Solution: (i) Two-digit numbers are from 10 to 90. Number of two-digit numbers = 90 - 9 = 81 ⇒ Probability of drawing a two-digit number = 81 90 = 9 10 (ii) Perfect square numbers between 1 and 90 are 1, 4, 9, 16, 25, 36, 49, 64, 81. Number of perfect squares = 9 ⇒ Probability of drawing a perfect square number = 9 90 = 1 ...

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 17 Question: (i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective? (ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective ? Given: Total number of bulbs = 20 Number of defective bulbs = 4 To Find: (i) Probability that the bulb drawn is defective. (ii) Probability that the second bulb drawn is not defective, given the first bulb was not defective and not replaced. Formula: Probability = Favorable Outcomes Total Outcomes Solution: (i) Probability that the bulb drawn is defective: Total number of outcomes = 20 Favorable outcomes (defective bulbs) = 4 Probability (defective) = 4 20 = 1 5 (ii) Probability that the second bulb is not defective: After drawing one non-de...

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 16 Question: 12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one. Given: Number of defective pens = 12 Number of good pens = 132 Total number of pens = 12 + 132 = 144 To Find: Probability of selecting a good pen Formula: Probability = Number of favorable outcomes Total number of possible outcomes Solution: Number of good pens = 132 Total number of pens = 144 Probability of selecting a good pen = 132 144 Simplifying the fraction by dividing both numerator and denominator by 12: 132 ÷ 12 144 ÷ 12 ⇒ 11 12 Result: The probability that the pen taken out is a good one is 11 12 . Next question solution: NCERT Class X Chapter 14: Probability Exercise...

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 15 Question: Five cards—the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.. (i) What is the probability that the card is the queen? . (ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen? Given: Five cards: 10, J, Q, K, A of diamonds. To Find: (i) Probability of picking the queen. (ii) (a) Probability of picking an ace after the queen is removed. (ii) (b) Probability of picking a queen after the queen is removed. Formula: Probability = Favorable Outcomes Total Outcomes Solution: (i) Probability of picking the queen: Total outcomes = 5 Favorable outcome (Queen) = 1 Probability (Queen) = 1 5 (ii) (a) Probability of picking an ace after the queen is removed: Total outcomes = 4 Favorable outcome (Ace) = 1 Probability (Ace) =...

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 14 Question: One card is drawn from a well-shuffled deck of 52 cards. Find 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 (vi) the queen of diamonds Given: A well-shuffled deck of 52 cards. To Find: 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 (vi) the queen of diamonds Formula: Probability = Number of favorable outcomes Total number of outcomes Solution: (i) Probability of getting a king of red colour: Number of kings of red colour = 2 (King of hearts and King of diamonds) Total number of cards = 52 Probability = 2 52 = 1 26 (ii) Probability of getting a face card: Number of face cards = 12 (4 Jacks + 4 Queens + 4 Kings) Total number of cards = 52 Probability = 12 52 = 3 13 (iii) Pro...

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 13 Question: A die is thrown once. Find the probability of getting: (i) a prime number; (ii) a number lying between 2 and 6; (iii) an odd number. Given: A die is thrown once. The sample space S = {1, 2, 3, 4, 5, 6} To Find: (i) Probability of getting a prime number. (ii) Probability of getting a number between 2 and 6. (iii) Probability of getting an odd number. Formula: Probability = Number of favorable outcomes Total number of outcomes Solution: (i) Prime numbers in S are {2, 3, 5}. Number of prime numbers = 3 Probability (prime number) = 3 6 = 1 2 (ii) Numbers between 2 and 6 are {3, 4, 5}. Number of such numbers = 3 Probability (number between 2 and 6) = 3 6 = 1 2 (iii) Odd numbers in S are {1, 3, 5}. Number of odd numbers = 3 Probability (odd number) = 3 6 = 1 2 Result: (i) Probability of getting a prime number = ...

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 12 Question: A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see Fig. 14.5), and these are equally likely outcomes. What is the probability that it will point at (i) 8? (ii) an odd number? (iii) a number greater than 2? (iv) a number less than 9? Given: Total number of outcomes = 8 (1, 2, 3, 4, 5, 6, 7, 8) To Find: (i) Probability of pointing at 8 (ii) Probability of pointing at an odd number (iii) Probability of pointing at a number greater than 2 (iv) Probability of pointing at a number less than 9 Formula: Probability = Number of favorable outcomes Total number of outcomes Solution: (i) Probability of pointing at 8: Number of favorable outcomes = 1 (only 8) Total number of outcomes = 8 Probability = 1 8 (ii) Probability of pointing at an odd number: Odd numbers are 1, 3, 5, 7 Number of favora...

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 11 Question: Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish. What is the probability that the fish taken out is a male fish? Given: Number of male fish = 5 Number of female fish = 8 Total number of fish = 5 + 8 = 13 To Find: Probability of selecting a male fish Formula: Probability = Number of favorable outcomes Total number of possible outcomes Solution: Number of favorable outcomes (selecting a male fish) = 5 Total number of possible outcomes (total number of fish) = 13 Probability of selecting a male fish = 5 13 Result: The probability that the fish taken out is a male fish is 5 13 Next question solution: NCERT Class X Chapter 14: Probability Exercise 14.1 Question 12 Explore more in Probability: Click this link to explore more NCERT Class X Chapter 1...

NCERT Class X Chapter 14: Probability Exercise 14.1 Question 10 Question: A piggy bank contains hundred 50p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin (i) will be a 50 p coin ? (ii) will not be a Rs 5 coin? Given: Number of 50p coins = 100 Number of Rs 1 coins = 50 Number of Rs 2 coins = 20 Number of Rs 5 coins = 10 To Find: (i) Probability that the coin will be a 50p coin. (ii) Probability that the coin will not be a Rs 5 coin. Formula: Probability = Number of favorable outcomes Total number of outcomes Solution: (i) Total number of coins = 100 + 50 + 20 + 10 = 180 Number of 50p coins = 100 Probability of getting a 50p coin = 100 180 = 5 9 (ii) Number of coins which are not Rs 5 coins = 180 - 10 = 170 Probability of not getting a Rs 5 coin = 170 180 = 17 ...