Classical Probability (Definition) MCQs Quiz | Class 10

This quiz covers essential concepts of Classical Probability for Class X Mathematics (Code 041), Unit VII: Statistics & Probability. You will find Multiple Choice Questions on Theoretical probability and the fundamental formula P(E)=favourable/total outcomes. Submit your answers and download a detailed PDF of your results.

Understanding Classical Probability

Probability is a branch of mathematics that deals with the likelihood of events occurring. It helps us quantify uncertainty. Classical probability, also known as theoretical probability, is one of the most fundamental ways to calculate the chances of an event.

Theoretical Probability: Definition and Formula

Theoretical probability relies on reasoning about all possible outcomes of an experiment without actually performing it. It assumes that all outcomes in the sample space are equally likely.

The formula for the theoretical probability of an event E is given by:

P(E) = (Number of Favourable Outcomes) / (Total Number of Possible Outcomes)

  • Event (E): A specific outcome or a set of outcomes.
  • Favourable Outcomes: The outcomes that satisfy the conditions of the event E.
  • Total Possible Outcomes (Sample Space): All possible outcomes of an experiment.

Key Properties of Probability

  1. Range of Probability: The probability of any event E always lies between 0 and 1, inclusive. That is, 0 <= P(E) <= 1.
  2. Sure Event: An event that is certain to happen has a probability of 1. For example, the probability of getting a number less than 7 when rolling a standard die.
  3. Impossible Event: An event that cannot happen has a probability of 0. For example, the probability of getting an 8 when rolling a standard die.
  4. Sum of Probabilities: The sum of the probabilities of all the elementary (individual) events of an experiment is always 1.

Examples Illustrating P(E) = Favourable / Total Outcomes

  • Coin Toss: When a fair coin is tossed, there are 2 possible outcomes (Head, Tail). The probability of getting a Head is 1 (favourable) / 2 (total) = 1/2.
  • Die Roll: When a fair six-sided die is rolled, there are 6 possible outcomes (1, 2, 3, 4, 5, 6).
    • Probability of getting an even number (2, 4, 6) = 3 (favourable) / 6 (total) = 1/2.
    • Probability of getting a prime number (2, 3, 5) = 3 (favourable) / 6 (total) = 1/2.
  • Drawing Cards: In a standard deck of 52 playing cards:
    • Probability of drawing a King = 4 (Kings) / 52 (total cards) = 1/13.
    • Probability of drawing a Red card = 26 (Red cards) / 52 (total cards) = 1/2.

Quick Revision Points

  • Probability measures the chance of an event.
  • Classical probability assumes equally likely outcomes.
  • P(E) = Favourable Outcomes / Total Outcomes.
  • Probability values are always between 0 and 1.
  • Sure event P = 1, Impossible event P = 0.

Practice Questions (Without Options)

  1. A bag contains 6 red, 4 blue, and 2 green marbles. What is the probability of drawing a blue marble?
  2. A number is chosen at random from integers 1 to 20. Find the probability that the number is a multiple of 5.
  3. What is the probability that a non-leap year has 53 Tuesdays?
  4. Two coins are tossed simultaneously. What is the probability of getting exactly one head?
  5. From a group of 5 boys and 3 girls, a student is selected at random. Find the probability that the selected student is a girl.