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Worksheet
Probability is a measure of the likelihood that an event will occur, calculated as the ratio of favorable outcomes to the total number of possible outcomes.
Probability - Practice Worksheet
Strengthen your foundation with key concepts and basic applications.
This worksheet covers essential long-answer questions to help you build confidence in Probability from Mathematics for Class X (Mathematics).
Questions
Define probability and explain its theoretical approach with an example.
Think about the basic definition of probability and how it applies to simple experiments like tossing a coin or rolling a die.
What is the difference between empirical and theoretical probability? Provide examples for each.
Consider how probability is calculated in real-life experiments versus ideal scenarios.
Explain the concept of complementary events in probability with an example.
Think about events that cover all possible outcomes and are mutually exclusive.
A bag contains 5 red, 3 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is not red? Explain your steps.
Consider using the complementary probability approach for an alternative solution.
Two dice are thrown simultaneously. What is the probability that the sum of the numbers on the two dice is 7? Explain your reasoning.
List all possible pairs of dice rolls that add up to 7 to find the number of favorable outcomes.
What is the probability of drawing a king or a queen from a well-shuffled deck of 52 cards? Explain your steps.
Count the total number of kings and queens in the deck to find the number of favorable outcomes.
A box contains 10 bulbs, of which 4 are defective. If one bulb is drawn at random, what is the probability that it is not defective? Explain your reasoning.
Subtract the number of defective bulbs from the total to find the number of non-defective bulbs.
Explain the concept of equally likely outcomes in probability with an example.
Consider simple experiments like tossing a coin or rolling a die where each outcome has the same chance.
A card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is a face card or a spade? Explain your steps.
Be careful not to double-count the face cards that are also spades.
A jar contains 24 marbles, some green and some blue. If the probability of drawing a green marble is 2/3, how many green marbles are in the jar? Explain your reasoning.
Use the given probability to set up a proportion and solve for the unknown quantity.
Probability - Mastery Worksheet
Advance your understanding through integrative and tricky questions.
This worksheet challenges you with deeper, multi-concept long-answer questions from Probability to prepare for higher-weightage questions in Class X Mathematics.
Questions
A bag contains 5 red, 3 blue, and 2 green marbles. If two marbles are drawn at random without replacement, what is the probability that both are red?
Consider the change in total number of marbles and red marbles after the first draw.
Compare and contrast empirical probability and theoretical probability with examples.
Think about how each type of probability is calculated and the basis for their calculations.
A die is rolled twice. What is the probability that the sum of the numbers on the two rolls is 7?
List all possible pairs that add up to 7 and count them.
Explain why the probability of an impossible event is 0 and a sure event is 1.
Consider the definitions of impossible and sure events in terms of favorable outcomes.
A card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is either a king or a heart?
Remember to subtract the overlap (king of hearts) to avoid double-counting.
Two coins are tossed simultaneously. What is the probability of getting at least one head?
List all possible outcomes and count those that meet the condition.
A box contains 10 bulbs, 4 of which are defective. If 3 bulbs are drawn at random without replacement, what is the probability that none are defective?
Calculate the probability step by step, adjusting the number of bulbs left after each draw.
What is the probability that a leap year selected at random will have 53 Sundays?
Focus on the extra days beyond the 52 weeks in a leap year.
A number is chosen at random from 1 to 50. What is the probability that it is a prime number?
Recall the definition of a prime number and count how many exist in the given range.
In a class of 40 students, 25 are girls. If a student is chosen at random, what is the probability that the student is a boy?
Subtract the number of girls from the total to find the number of boys.
Probability - Challenge Worksheet
Push your limits with complex, exam-level long-form questions.
The final worksheet presents challenging long-answer questions that test your depth of understanding and exam-readiness for Probability in Class X.
Questions
A bag contains 5 red, 3 blue, and 2 green marbles. If two marbles are drawn at random without replacement, what is the probability that both marbles are of the same color?
Consider the total number of marbles and how drawing one affects the next draw.
In a game, a player rolls two dice. If the sum is 7 or 11, the player wins. What is the probability of winning on the first roll?
Enumerate all possible pairs that sum to 7 or 11.
A card is drawn from a deck of 52 cards. What is the probability that it is either a heart or a queen?
Remember to subtract the probability of the intersection of the two events.
Two coins are tossed simultaneously. What is the probability of getting at least one head?
It's easier to consider the opposite of 'at least one head'.
A die is rolled twice. What is the probability that the sum of the numbers is divisible by 3?
Consider all pairs (1,2), (2,1), etc., that sum to multiples of 3.
In a lottery, a ticket has 5 different numbers from 1 to 50. What is the probability of winning if the ticket matches all 5 numbers drawn?
This is a combination problem where order does not matter.
A box contains 10 bulbs, 4 of which are defective. If 3 bulbs are drawn at random, what is the probability that exactly one is defective?
Think in terms of combinations for selecting defective and non-defective bulbs.
What is the probability that a randomly chosen two-digit number is divisible by both 2 and 5?
Numbers divisible by both 2 and 5 are divisible by their LCM, which is 10.
A family has two children. Given that at least one is a boy, what is the probability that both are boys?
List all possible gender combinations and exclude the ones that don't meet the condition.
A number is chosen at random from the first 100 natural numbers. What is the probability that it is a perfect square but not a perfect cube?
First, find how many numbers are perfect squares, then subtract those that are both squares and cubes.
Explore real-world applications of trigonometry in measuring heights, distances, and angles in various fields such as astronomy, navigation, and architecture.
Explore the properties, theorems, and applications of circles in geometry, including tangents, chords, and angles subtended by arcs.
Explore the concepts of calculating areas related to circles, including sectors, segments, and combinations with other geometric shapes.
Explore the concepts of calculating surface areas and volumes of various geometric shapes, including cubes, cylinders, cones, and spheres, to solve real-world problems.
Statistics is the chapter that deals with the collection, analysis, interpretation, presentation, and organization of data.
