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Chapter Analysis
Intermediate16 pages • EnglishQuick Summary
The chapter on Probability in Class 10 Mathematics introduces the theoretical concept of probability and distinguishes it from experimental probability. It explains the fundamental principle where probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. Key examples and exercises are given to illustrate how probability measures the likelihood of various events.
Key Topics
- •Theoretical probability
- •Complement of an event
- •Experimental probability
- •Probability as a measure of likelihood
- •Equally likely outcomes
- •Elementary events
- •Impossible and sure events
- •Empirical probability
Learning Objectives
- ✓Understand the concept of probability as a measure of chance.
- ✓Differentiate between theoretical and experimental probability.
- ✓Calculate the probability of simple events.
- ✓Explore the relationship between an event and its complement.
- ✓Identify examples of equally likely outcomes.
- ✓Apply probability concepts to real-life situations.
Questions in Chapter
Complete the following statements: (i) Probability of an event E + Probability of the event ‘not E’ = _______. (ii) The probability of an event that cannot happen is ______. Such an event is called _______. (iii) The probability of an event that is certain to happen is ______. Such an event is called _______. (iv) The sum of the probabilities of all the elementary events of an experiment is ______. (v) The probability of an event is greater than or equal to ______ and less than or equal to ______.
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Which of the following experiments have equally likely outcomes? Explain. (i) A driver attempts to start a car. The car starts or does not start. (ii) A player attempts to shoot a basketball. She/he shoots or misses the shot. (iii) A trial is made to answer a true-false question. The answer is right or wrong. (iv) A baby is born. It is a boy or a girl.
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Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?
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Which of the following cannot be the probability of an event? (A) 2/3 (B) –1.5 (C) 15% (D) 0.7
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If P(E) = 0.05, what is the probability of ‘not E’?
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A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out (i) an orange flavoured candy? (ii) a lemon flavoured candy?
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It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?
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A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red? (ii) not red?
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A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red? (ii) white? (iii) not green?
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A piggy bank contains hundred 50p coins, fifty ` 1 coins, twenty ` 2 coins and ten ` 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 50p coin? (ii) will not be a ` 5 coin?
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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?
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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, 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?
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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.
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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
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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?
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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.
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(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?
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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.
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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?
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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?
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(i) Complete the following table: [Event : ‘Sum on 2 dice’ 2 3 4 5 6 7 8 9 10 11 12, Probability] (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 1/11. Do you agree with this argument? Justify your answer.
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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.
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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?
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Additional Practice Questions
Suppose there is a bag with 6 blue balls, 3 red balls, and 1 yellow ball. What is the probability of drawing a red ball?
easyAnswer: The total number of balls is 10, and there are 3 red balls. Therefore, the probability of drawing a red ball is 3/10.
A standard six-sided die is rolled once. What is the probability of rolling a number greater than 5?
easyAnswer: The only number greater than 5 on a six-sided die is 6. Therefore, the probability of rolling a number greater than 5 is 1/6.
If two dice are rolled simultaneously, what is the probability that the sum is equal to 7?
mediumAnswer: The pairs that sum to 7 are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). Therefore, there are 6 favourable outcomes out of a total of 36 outcomes, making the probability 6/36 = 1/6.
What is the probability of drawing an ace from a standard deck of 52 playing cards?
easyAnswer: There are 4 aces in a deck of 52 cards. Therefore, the probability of drawing an ace is 4/52 = 1/13.
A bag contains 20 marbles: 8 are green, 7 are blue, and 5 are red. If a marble is drawn randomly, what is the probability that it is neither green nor blue?
mediumAnswer: There are 5 red marbles, which are neither green nor blue. Therefore, the probability is 5/20 = 1/4.
In a class of 30 students, what is the probability that a student chosen at random has a birthday in February?
mediumAnswer: Assuming a non-leap year with 365 days, the probability that a student's birthday is in February is 28/365, considering 28 days in February.
What is the probability of drawing two consecutive kings from a deck of cards without replacement?
hardAnswer: The probability of drawing the first king is 4/52. If the first card drawn is a king, the probability of drawing a second king is 3/51. Therefore, the probability of both events occurring is (4/52) * (3/51) = 1/221.
What is the probability of drawing a heart from a standard deck of cards?
easyAnswer: There are 13 hearts in a deck of 52 cards. Therefore, the probability of drawing a heart is 13/52 = 1/4.
If a single coin is flipped three times, what is the probability of getting exactly two heads?
mediumAnswer: The successful outcomes are HHT, HTH, and THH. Therefore, there are 3 favourable outcomes out of 8 total outcomes, making the probability 3/8.
A game of chance consists of spinning a wheel divided into 10 equal sectors numbered 1 to 10. What is the probability of landing on an even number?
easyAnswer: The even numbers on the wheel are 2, 4, 6, 8, and 10. There are 5 even numbers, so the probability is 5/10 = 1/2.