Class 10 Maths MCQ Test – Probability (Chapter 14) | Full Chapter Test
Class 10 Mathematics – Chapter: Probability (Detailed Notes)
These notes are designed for CBSE, GSEB and board exam preparation. Includes all concepts, formulas, and exam-oriented explanations.
1. What is Probability?
Probability means the chance of occurrence of an event.
- Probability ranges between 0 and 1
- 0 → Impossible event
- 1 → Certain event
Example:
- Getting head in a coin toss → probability = 1/2
- Sun rising in east → probability = 1
- Getting 7 on a dice → probability = 0
2. Experiment, Outcome and Event
- Experiment: An action with uncertain result (e.g., tossing a coin)
- Outcome: Possible result (Head or Tail)
- Event: A group of outcomes
Example: Rolling a die
- Sample space: {1,2,3,4,5,6}
- Event (getting even number): {2,4,6}
3. Sample Space
The set of all possible outcomes is called sample space.
Notation: S
Example:
- Coin → S = {H, T}
- Dice → S = {1,2,3,4,5,6}
4. Classical Probability Formula
If all outcomes are equally likely:
\( P(E) = \frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}} \)
Important:
- \( 0 \leq P(E) \leq 1 \)
- \( P(\text{Sure event}) = 1 \)
- \( P(\text{Impossible event}) = 0 \)
5. Types of Events
1. Sure Event
Event that will definitely occur.
2. Impossible Event
Event that cannot occur.
3. Simple Event
Event with only one outcome.
4. Compound Event
Event with more than one outcome.
6. Complementary Events
If E is an event, then its complement is denoted by \( E' \)
\( P(E) + P(E') = 1 \)
Example:
- Event: Getting a head
- Complement: Not getting a head (tail)
7. Probability with Dice
Total outcomes = 6
- Even numbers → {2,4,6} → Probability = 3/6 = 1/2
- Prime numbers → {2,3,5} → Probability = 3/6 = 1/2
- Number > 4 → {5,6} → Probability = 2/6 = 1/3
8. Probability with Cards
Total cards = 52
- Hearts = 13
- Spades = 13
- Diamonds = 13
- Clubs = 13
Examples:
- Probability of getting a heart = 13/52 = 1/4
- Probability of getting a king = 4/52 = 1/13
- Probability of red card = 26/52 = 1/2
9. Probability with Coins
Single coin:
- S = {H, T}
- P(H) = 1/2
Two coins:
- S = {HH, HT, TH, TT}
- P(2 heads) = 1/4
- P(at least one head) = 3/4
10. Important Tips for Exams
- Always write sample space first
- Check if outcomes are equally likely
- Simplify fraction at the end
- Use complement when easier
- Avoid calculation mistakes in counting outcomes
11. Solved Examples
Q1. Find probability of getting a number divisible by 3 when a die is thrown.
Numbers divisible by 3 → {3,6}
\( P = \frac{2}{6} = \frac{1}{3} \)
Q2. A card is drawn from a deck. Find probability of getting a queen.
Total queens = 4
\( P = \frac{4}{52} = \frac{1}{13} \)
Q3. Find probability of not getting a tail in coin toss.
\( P(\text{not tail}) = P(\text{head}) = \frac{1}{2} \)
⬇️ Attempt the test given below after revising these notes
Class 10 Mathematics
Chapter 14 : Probability | Full Chapter MCQ Test
Class 10 Mathematics Chapter 14: Probability
Probability is one of the most important and scoring chapters in Class 10 Mathematics. It helps students understand how to measure uncertainty and predict outcomes in real-life situations. This chapter forms the base for higher studies in statistics and data science.
Learning Outcomes
After completing this chapter, students will be able to:
- Understand the concept of probability as a measure of chance.
- Define experiment, outcome, event, and sample space.
- Identify equally likely outcomes in experiments.
- Apply the classical probability formula:
- P(E) = Number of favourable outcomes / Total outcomes
- Find probability in experiments involving coins, dice, and playing cards.
- Understand complementary events and use:
- P(E) + P(E') = 1
- Solve real-life problems using probability concepts.
Real Life Applications
Probability is widely used in everyday life and various fields:
- Weather Forecasting: Predicting chances of rain or storms.
- Games: Used in games like cards, dice, and lotteries.
- Sports: Predicting winning chances of teams.
- Insurance: Calculating risk and premium.
- Medical Field: Estimating success rate of treatments.
- Business: Decision making based on probability of outcomes.
Common Mistakes Students Make
- Not writing the complete sample space.
- Counting favourable outcomes incorrectly.
- Forgetting that probability cannot be negative or greater than 1.
- Confusing complementary events.
- Making errors in cases like “at least”, “at most”, etc.
- Not simplifying the final answer.
Conclusion
Probability is a simple yet powerful chapter. With proper understanding and practice, students can score full marks. Focus on clarity of concepts, accurate counting of outcomes, and regular practice of different types of questions.
Class 10 Mathematics Chapter 14: Probability
10 Detailed Solved Examples
Find the probability of getting a head when a coin is tossed.
Solution:
Sample space S = {H, T}
Favourable outcomes = 1 (H)
P(H) = 1/2
Find the probability of getting an even number when a die is thrown.
Solution:
S = {1,2,3,4,5,6}
Even numbers = {2,4,6} → 3 outcomes
P = 3/6 = 1/2
A card is drawn from a deck. Find probability of getting a king.
Solution:
Total cards = 52
Kings = 4
P = 4/52 = 1/13
Find probability of not getting a head.
Solution:
P(H) = 1/2
P(not H) = 1 − 1/2 = 1/2
Find probability of getting two heads when two coins are tossed.
Solution:
S = {HH, HT, TH, TT}
Favourable = 1 (HH)
P = 1/4
Find probability that sum is 7 when two dice are thrown.
Solution:
Total outcomes = 36
Favourable = (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6 outcomes
P = 6/36 = 1/6
Find probability of getting a prime number.
Solution:
Prime numbers = {2,3,5} → 3 outcomes
P = 3/6 = 1/2
Find probability of getting at least one head when two coins are tossed.
Solution:
S = {HH, HT, TH, TT}
Favourable = 3 (HH, HT, TH)
P = 3/4
Find probability of getting a number less than 4 on a die.
Solution:
Numbers = {1,2,3} → 3 outcomes
P = 3/6 = 1/2
Find probability of getting at least one tail when two coins are tossed.
Solution:
P(no tail) = P(HH) = 1/4
P(at least one tail) = 1 − 1/4 = 3/4
10 Detailed FAQs
Probability is the measure of likelihood of an event occurring, ranging between 0 and 1.
It is the set of all possible outcomes of an experiment.
An event is a subset of the sample space.
It is defined as favourable outcomes divided by total outcomes when all outcomes are equally likely.
If E is an event, then its complement E' is given by P(E') = 1 − P(E).
No, probability always lies between 0 and 1.
It helps in decision making and predicting outcomes in real life.
Outcomes having the same chance of occurring.
An event that will definitely occur, with probability 1.
An event that cannot occur, with probability 0.
Comments
Post a Comment