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Basic Concepts of Probability Quiz - CBSE Class 9 Mathematics

Free practice quiz: Basic Concepts of Probability (CBSE Class 9 Mathematics). 16 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 9 Mathematics practice quiz has 16 multiple-choice questions on Basic Concepts of Probability, and 16 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Probability of an Event

  • Probability measures how likely an event is to happen, when all outcomes are equally likely.
  • Count the outcomes that suit the event, then divide by the total number of possible outcomes.
Probability of event E
\[P(E) = \frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}\]
With letters
\[P(E) = \frac{m}{n}\]

Common mistake: Counting only the outcomes that are not favourable as the total, instead of counting every possible outcome in the denominator.

Range and Complement Rule

  • Probability is always between 0 and 1. An impossible event has probability 0, a sure event 1.
  • The event 'not E' happens exactly when E does not happen. Their probabilities add to 1.
Range of probability
\[0 \le P(E) \le 1\]
Complement rule
\[P(\text{not } E) = 1 - P(E)\]
Sum of complements
\[P(E) + P(\bar{E}) = 1\]

Common mistake: Giving a probability greater than 1 or negative, or forgetting to subtract from 1 when the question asks for the opposite event.

Listing All Possible Outcomes

  • First write the full list of outcomes, called the sample space, before counting favourable ones.
  • Know standard objects well: a coin's faces, a die's faces, card suits and colours, days, months, letters.
Total outcomes
\[n = \text{size of the sample space}\]

Common mistake: Missing some outcomes while listing, for example forgetting that a card deck has both red and black suits or both vowels and consonants.

Combined Experiments

  • When doing several experiments together, every outcome of one pairs with every outcome of the other.
  • For independent experiments, the probability that both events happen is the product of their probabilities.
Total outcomes of combined experiment
\[\text{Total} = a \times b\]
Both independent events happen
\[P(A \text{ and } B) = P(A) \times P(B)\]

Common mistake: Adding probabilities instead of multiplying when both events must happen, or treating HT and TH as the same outcome.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. What is the probability of drawing a heart from a standard deck of 52 cards?

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    Answer: B. 1/4

    There are 4 suits in a deck, each with an equal probability. Therefore, the probability of drawing a heart is 1/4.

  2. What is the probability that a randomly selected day of the week will be a weekend day?

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    Answer: B. 2/7

    There are 7 days in a week, and 2 are weekend days (Saturday and Sunday), so the probability is 2/7.

  3. What is the probability of getting an even number when rolling a standard six-sided die?

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    Answer: A. 1/2

    There are 3 even numbers (2, 4, 6) on a die, so the probability is 3/6 = 1/2.

  4. What is the probability that a randomly chosen month will have 31 days?

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    Answer: A. 7/12

    There are 7 months with 31 days (January, March, May, July, August, October, December), so the probability is 7/12.

  5. If a die is tossed twice, what is the probability that both results will be 5?

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    Answer: A. 1/36

    The probability of each roll being 5 is 1/6. For two rolls, it's (1/6) x (1/6) = 1/36.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. What is the probability of rolling a 4 on a standard six-sided die?
  2. If you flip a fair coin, what is the probability of getting heads?
  3. In a class of 30 students, 18 are boys. What is the probability that a randomly selected student is a girl?
  4. A bag contains 5 red balls and 3 blue balls. What is the probability of drawing a blue ball?
  5. If two coins are tossed, what is the probability of getting two heads?
  6. What is the probability of drawing a king from a standard deck of cards?
  7. In a group of 120 people, 60 are males. What is the probability of randomly selecting a female?
  8. What is the probability of drawing a queen from a well-shuffled deck of cards?
  9. What is the probability of randomly drawing a vowel from the alphabet?
  10. What is the probability of drawing a black card from a deck of 52 cards?
  11. What is the probability of drawing an ace of spades from a standard deck of cards?

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