Enhanced Curriculum Support
This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:
Comprehensive Learning: This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.
Critical Thinking and Reasoning: Value-Based and HOTS questions promote critical thinking and reasoning abilities. These skills are crucial for students to tackle complex problems and make informed decisions.
Exam Preparedness: Sample Question Papers and Practice Questions provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.
Ethical and Moral Development: Value-Based Questions integrate ethical and moral lessons into the learning process, helping in the overall development of students' character and social responsibility. By incorporating these diverse elements, Enhanced Curriculum Support aims to provide a robust and well-rounded knowledge, preparing students for both academic success and real-world challenges.
Sample Questions
Sec A
(1) If a letter is chosen from English alphabet, then the probability of being vowel.
(A)
(B)
(C)
(D)
(2) If a coin is tossed once, what is the probability of getting a tail? (A) 0 (B)
(3) A die is rolled once. Find the probability of getting a number less than 4. (A)
(4) If a letter is chosen at random from the word “MATHEMATICS”, what is the probability of choosing the letter 'A'?
(5) What is the probability of drawing a king from a well-shuffled deck of 52 cards? (A)
(6) What is the probability of an impossible event? (A) 1 (B) 0 (C) 0.5 (D) Depends on the experiment
Sec B
(1) A bag contains 7 green balls, 4 blue balls, 5 red balls and 4 yellow balls. One ball is drawn out randomly. Find the probability of getting red ball.
(2) A bag contains 5 red, 3 blue, and 2 green marbles. One marble is picked at random. What is the probability of it being (a) blue (b) not green?
(3) An experiment consists of rolling a die once. List the sample space and find the probability of getting a multiple of 3.
(4) Out of 50 students in a class, 30 are boys. If one student is chosen at random, what is the probability of selecting a girl?
(5) In a game, a spinner is divided into 8 equal sectors numbered from 1 to 8. What is the probability that it lands on:
(a) an even number
(b) a number greater than 6?
(6) The probability of getting a prime number when a die is rolled is
Sec C
(1) A bag contains 6 black balls and 4 white balls. A ball is drawn at random, noted, and then replaced. The experiment is repeated 200 times and black ball comes up 150 times. (a) Find the theoretical probability of drawing a black ball. (b) Compare it with experimental probability. (c) What can you say about the outcome as the number of trials increases?
(2) A game involves spinning a wheel with colors: 3 red, 2 green, and 5 blue sections. (a) What is the probability of landing on red? (b) What is the probability of not landing on blue? (c) Is this experiment fair? Justify.
(3) Letters of the word “PROBABILITY” are written on separate cards and shuffled. (a) What is the probability of drawing the letter 'B'? (b) What is the probability of drawing a vowel? (c) What is the total number of equally likely outcomes?
(4) A die is thrown 120 times. The following outcomes were recorded:
1 – 20 times, 2 – 18 times, 3 – 22 times, 4 – 20 times, 5 – 18 times, 6 – 22 times.
(a) Find the experimental probability of getting a 3. (b) What is the total of all probabilities? (c) How does it compare with theoretical probability?
(5) Two coins are tossed together 100 times and the following results were observed:
Two heads: 24 times
One head: 52 times
No head: 24 times
(a) Find the experimental probability of each event.
(b) What is the theoretical probability of getting exactly one head?
(c) Comment on the difference.
Value Based Questions
Problem 1
A game at a village fair promises that “everyone is likely to win.” However, the spinner used in the game has 6 sections, with only one of them being a “Win” section. Do you think this claim is fair or ethical? Justify your answer using the concept of probability.
Problem 2
Ravi always loses in a dice-based game organized by his friend. Later, he finds out the die was tampered to land mostly on 6. What values are violated in this case? How does understanding of probability help identify fair play?
Problem 3
A student is told she has a “zero chance” of winning a scholarship. But the scholarship is based on a random draw. Why is this statement incorrect? What does it teach us about judging possibilities and respecting fairness?
Problem 4
In a school competition, every participant is given a chance to pick a chit from a box to decide their turn. The teacher ensures all chits are identical and well-mixed. How does this promote fairness? What values does this method uphold in the context of probability?
HOTS
Q1
A bag contains 3 red balls and 2 blue balls. One ball is drawn at random. Without calculating, can you say whether the probability of drawing a red ball is more than that of a blue ball? Justify your reasoning based on your understanding of “equally likely outcomes.”
Q2
A coin is tossed 500 times and heads appears 310 times. Is the coin fair? Explain your answer with respect to the concept of large number of trials.
Practice Questions
Choose the correct option.
Questions
(1) A card is drawn from a standard deck of 52 cards. What is the probability of drawing a queen?
(A)
(2) A die is rolled. What is the probability of getting a number greater than 4?
(A)
(3) What is the probability of getting a consonant when a letter is selected from the word “SCIENCE”?
(A)
(4) Which of the following is a certain event?
(A) Getting a number less than 7 on a die (B) Getting a tail when a coin is tossed (C) Getting an odd number when a die is rolled (D) Getting red card from a green box
(5) What is the range of probability of any event?
(A) Between 0 and 2 (B) Between –1 and 1 (C) Between 0 and 1 (D) Any positive value
Fill the given blanks.
Questions
(1) The probability of an impossible event is ?.
(2) If all outcomes are equally likely, the formula for probability is: P(E) = ?.
(3) A die has ? possible outcomes when rolled once.
(4) The probability of getting a vowel from the word “PROBABILITY” is ?.
(5) When an unbiased coin is tossed once, the outcomes are ? and ?.
Answer the following questions.
Questions
(1) A bag contains 4 red, 5 black, and 3 white balls. One ball is taken out randomly. Find the probability of drawing:
(a) A red ball
(b) A black ball
(c) A ball which is not white
(2) An experiment consists of tossing two coins simultaneously. List the sample space and find the probability of getting:
(a) two heads
(b) at least one head
(c) no heads
(3) In a class of 40 students, 16 like cricket, 12 like football, and the rest like badminton. A student is chosen at random. What is the probability that the student likes:
(i) Cricket
(ii) Badminton
(iii) Not football
(4) A spinner is divided into 6 equal parts and numbered from 1 to 6. What is the probability of getting:
(a) a prime number
(b) an even number
(c) a number greater than 5
(5) A survey of 200 students showed that 60 preferred tea, 90 preferred coffee, and 50 liked neither. If one student is selected at random, what is the probability that the student likes:
(a) Tea
(b) Coffee
(c) At least one of the two drinks
Case Based Questions
Q1
In a classroom, students were asked to toss a coin 100 times and record the number of heads and tails.
Group A got 48 heads and 52 tails.
Group B got 50 heads and 50 tails.
Group C got 38 heads and 62 tails.
(a) Which group’s result shows the best example of equally likely outcomes?
(b) As the number of trials increases, what pattern do you observe in the frequency of outcomes?
(c) Which group's experiment shows a possible bias? Why do you think so?
Q2
At a school fair, a spinning wheel has 8 equal sections numbered from 1 to 8. A prize is awarded if the spinner lands on a prime number.
(a) What is the total number of possible outcomes?
(b) What are the favourable outcomes for winning a prize?
(c) Find the probability of winning the prize.
(d) Is winning the prize more or less likely than losing? Explain.