Class 10 Math Probability MCQ Test

Class 10 Math Probability MCQ Test: Enhance your understanding with free online multiple-choice questions for CBSE Class 10 Math Chapter 14. Master the fundamental concepts of probability, including theoretical probability, experimental probability, and probability calculations. Ideal for CBSE exam preparation and competitive tests.

Math Probability MCQ Test Quiz

Time: 10 Minutes for 10 Question.

10th Math: Probability

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About Probability

Chapter 15 of the CBSE Class 10 Math curriculum, titled “Probability,” introduces the fundamental principles of probability and its applications. This chapter covers key concepts such as theoretical and experimental probability, as well as various methods for calculating the likelihood of events. The free MCQ quiz provided in this chapter will help students solidify their understanding and prepare effectively for their CBSE examinations.

Key Concepts Covered:

Basic Concepts of Probability:
- Definition: Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1.
- Probability Formula: For an event $E$
  
  $E$ , the probability $P(E)$
  
  $P (E)$ is given by: $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$
  
  $P (E) = Total number of outcomes Number of favorable outcomes$
- Range of Probability: Probability values range from 0 (impossible event) to 1 (certain event).
Theoretical Probability:
- Simple Events: The probability of a simple event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
- Example: If a die is rolled, the probability of getting a 3 is $\frac{1}{6}$
  
  $6 1$ because there is one favorable outcome and six possible outcomes.
Experimental Probability:
- Definition: Experimental probability is based on actual experiments or trials. It is calculated as: $P(E) = \frac{\text{Number of times event occurred}}{\text{Total number of trials}}$
  
  $P (E) = Total number of trials Number of times event occurred$
- Example: If a coin is flipped 100 times and lands on heads 55 times, the experimental probability of getting heads is $\frac{55}{100} = 0.55$
  
  $100 55 = 0.55$ .
Probability of Compound Events:
- Complementary Events: The probability of the complement of an event $E$
  
  $E$ (i.e., $E’$
  
  $E^{'}$ ) is given by: $P(E’) = 1 – P(E)$
  
  $P (E^{'}) = 1 - P (E)$
- Union of Events: For two events $A$
  
  $A$ and $B$
  
  $B$ , the probability of $A \cup B$
  
  $A \cup B$ (either event $A$
  
  $A$ or $B$
  
  $B$ occurring) is: $P(A \cup B) = P(A) + P(B) – P(A \cap B)$
  
  $P (A \cup B) = P (A) + P (B) - P (A \cap B)$
- Intersection of Events: For two events $A$
  
  $A$ and $B$
  
  $B$ , the probability of $A \cap B$
  
  $A \cap B$ (both events occurring) is: $P(A \cap B) = P(A) \times P(B) \text{ (if $A$ and $B$ are independent)}$
  
  $P (A \cap B) = P (A) \times P (B) (if A and B are independent)$
Conditional Probability:
- Definition: The probability of event $A$
  
  $A$ occurring given that event $B$
  
  $B$ has occurred is: $P(A | B) = \frac{P(A \cap B)}{P(B)}$
  
  $P (A ∣ B) = P ( B ) P ( A \cap B )$
- Example: If a card is drawn from a deck and it is known to be a spade, the probability that it is a king is $\frac{1}{13}$
  
  $13 1$ .
Application Problems:
- Example 1: A bag contains 3 red balls and 2 green balls. What is the probability of drawing a red ball?
  - Solution: Probability = $\frac{3}{5}$
    
    $5 3$ .
- Example 2: If a die is rolled once, what is the probability of getting an even number?
  - Solution: Probability = $\frac{3}{6} = \frac{1}{2}$
    
    $6 3 = 2 1$ .
Probability in Real-Life Situations:
- Games and Experiments: Applying probability to predict outcomes in games, experiments, and real-life scenarios.
- Example: Determining the likelihood of winning a game based on the rules and possible outcomes.

Quiz Structure:

The MCQ quiz for this chapter includes a series of questions designed to test students’ understanding of probability concepts, including theoretical and experimental probability, compound events, and conditional probability. Questions cover calculation techniques, interpretation of results, and real-life applications. The interactive format allows students to practice and assess their knowledge effectively.

Conclusion:

Practicing with the Class 10 Math Probability MCQ Test Chapter 15 is an excellent way for CBSE students to reinforce their understanding of probability concepts. This chapter provides a comprehensive overview of probability theory, including calculations for various types of events and practical applications. The MCQ quiz helps ensure students are well-prepared for their academic assessments and competitive exams.

Sanjay Kumar

Math educator (6-12) with an MSc from Delhi University and quiz content creator at QuizRanker.org.