Samacheer Kalvi Class 9 Maths Solutions Chapter 9 Probability Exercise 9.3

I. Multiple Choice Questions.

Question 1. A number between 0 and 1 that is used to measure uncertainty is called .........
(a) Random variable
(b) Trial
(c) Simple event
(d) Probability
Answer: (d) Probability
In simple words: Probability is a number that helps us understand how likely something is to happen. It always stays between 0 and 1.

🎯 Exam Tip: Always remember that a probability of 0 means an event is impossible, while a probability of 1 means it is certain to happen.

Question 2. Probability lies between .........
(a) -1 and +1
(b) 0 and 1
(c) 0 and n
(d) 0 and \( \infty \)
Answer: (b) 0 and 1
In simple words: The value of any probability will always be from 0 to 1. It can never be a negative number or greater than 1.

🎯 Exam Tip: It is important to know that probability is expressed as a number between 0 and 1, inclusive, indicating the likelihood of an event.

Question 3. The probability based on the concept of relative frequency theory is called .......
(a) Empirical probability
(b) Classical probability
(c) Both (a) and (b)
(d) Neither (a) nor (b)
Answer: (a) Empirical probability
In simple words: Empirical probability is found by doing an experiment many times and seeing how often an event happens. It relies on real-world tests, not just theories.

🎯 Exam Tip: Empirical probability is often used in real-world situations, like predicting weather or market trends, because it comes from observed data.

Question 4. The probability of an event cannot be ..........
(a) Equal to zero
(b) Greater than zero
(c) Equal to one
(d) Less than zero
Answer: (d) Less than zero
In simple words: Probability can be zero, one, or any number between them, but it can never be a negative number. This is because negative values do not make sense for how often something might happen.

🎯 Exam Tip: Always check that your calculated probability is a positive value between 0 and 1. If it's negative or more than 1, you've made a mistake.

Question 5. The probability of all possible outcomes of a random experiment is always equal to .........
(a) One
(b) Zero
(c) Infinity
(d) Less than one
Answer: (a) One
In simple words: When you add up the probabilities of all the possible things that can happen in an experiment, the total must always be 1. This means that something from the possible outcomes will definitely happen.

🎯 Exam Tip: The sum of probabilities for all outcomes in a sample space must always be exactly 1, representing 100% certainty that one of these outcomes will occur.

Question 6. If A is any event in S and its complement is A' then P(A') is equal to .........
(a) 1
(b) 0
(c) \( 1-A \)
(d) \( 1-P(A) \)
Answer: (d) \( 1-P(A) \)
In simple words: The probability of an event not happening (called its complement) is found by subtracting the probability of the event happening from 1. This is because an event either happens or it doesn't.

🎯 Exam Tip: Understanding complementary events is crucial for solving many probability problems, as \( P(A') = 1 - P(A) \) is a fundamental rule.

Question 7. Which of the following cannot be taken as probability of an event?
(a) 0
(b) 0.5
(c) 1
(d) -1
Answer: (d) -1
In simple words: Probability cannot be negative. It must always be between 0 (impossible) and 1 (certain). A negative number like -1 cannot represent a chance of something happening.

🎯 Exam Tip: Always remember that probability values are non-negative. If you calculate a negative probability, it indicates an error in your calculation.

Question 8. A particular result of an experiment is called .........
(a) Trial
(b) Simple event
(c) Compound event
(d) Outcome
Answer: (d) Outcome
In simple words: When you do an experiment, like flipping a coin, each possible result (like heads or tails) is called an outcome. It's what actually happens.

🎯 Exam Tip: Clearly distinguishing between a trial, an event, and an outcome is essential for correctly setting up and solving probability problems.

Question 9. A collection of one or more outcomes of an experiment is called .........
(a) Event
(b) Outcome
(c) Sample point
(d) None of the options
Answer: (a) Event
In simple words: An event is a group of one or more outcomes from an experiment. For example, if you roll a dice, getting an even number (2, 4, or 6) is an event.

🎯 Exam Tip: An event is a subset of the sample space, which means it contains specific outcomes that we are interested in.

Question 10. The six faces of the dice are called equally likely if the dice is .........
(a) Small
(b) Fair
(c) Six-faced
(d) Round
Answer: (b) Fair
In simple words: A fair dice means that each of its six faces has an equal chance of landing up. This is very important for calculating probabilities correctly in games.

🎯 Exam Tip: The term "fair" is used when all possible outcomes of an experiment have the same probability of occurring, ensuring no bias.