## CBSE Class 10 Maths Notes Chapter 15 Probability

here are the important topics covered in CBSE Class 10 Maths Chapter 15 – Probability:

- Introduction to Probability
- Calculating Probability
- Basic Concepts of Probability
- Probability Distribution
- Experimental Probability
- Theoretical Probability
- Rules of Probability
- Dependent and Independent Events
- Mutually Exclusive Events
- Complementary Events

In this chapter, you will learn the basic concept of probability, how to calculate probability, different types of probability, and their rules. You will also learn about the probability distribution, dependent and independent events, mutually exclusive events, and complementary events. Understanding these concepts will help you solve probability problems and make predictions about the likelihood of future events.

**CBSE Class 10 Maths Important Questions Chapter 15 Probability**

Here are some important questions for CBSE Class 10 Maths Chapter 15 Probability:

- What is probability?
- What is the probability of an impossible event?
- What is the probability of a certain event?
- How do you calculate the probability of an event?
- What is the difference between experimental probability and theoretical probability?
- What is the difference between mutually exclusive and non-mutually exclusive events?
- What is the difference between independent and dependent events?
- If two dice are rolled together, what is the probability of getting a sum of 9?
- If a card is drawn from a deck of cards, what is the probability of getting a red card?
- What is the probability of getting a head when a coin is tossed?

Answers:

- Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
- The probability of an impossible event is 0.
- The probability of a certain event is 1.
- The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
- Experimental probability is based on the results of an actual experiment or trial, while theoretical probability is based on the theoretical probability of an event occurring.
- Mutually exclusive events are events that cannot occur at the same time, while non-mutually exclusive events can occur at the same time.
- Independent events are events where the occurrence of one event does not affect the probability of the other event occurring, while dependent events are events where the occurrence of one event affects the probability of the other event occurring.
- The probability of getting a sum of 9 when two dice are rolled together is 4/36 or 1/9.
- The probability of getting a red card when a card is drawn from a deck of cards is 26/52 or 1/2.
- The probability of getting a head when a coin is tossed is 1/2.

**CBSE Class 10 Maths Important Questions Answers Chapter 15 Probability**

- A coin is tossed twice. What is the probability of getting at least one head? Answer: The possible outcomes of tossing a coin twice are {HH, HT, TH, TT}. Out of these, the outcomes which have at least one head are {HH, HT, TH}. So, the probability of getting at least one head = 3/4.
- Two dice are rolled together. What is the probability that the sum of the numbers on the dice is greater than 8? Answer: The possible outcomes of rolling two dice are {1,1}, {1,2}, {1,3}, …, {6,6}. There are 36 possible outcomes. Out of these, the outcomes in which the sum of the numbers on the dice is greater than 8 are {3,6}, {4,5}, {4,6}, {5,4}, {5,5}, {5,6}, {6,3}, {6,4}, {6,5}, {6,6}. So, the probability of getting a sum greater than 8 = 10/36 = 5/18.
- In a class, there are 20 girls and 15 boys. If a student is selected at random, what is the probability that the student selected is a boy? Answer: Total number of students in the class = 20 + 15 = 35. Number of boys in the class = 15. So, the probability of selecting a boy = 15/35 = 3/7.
- A bag contains 5 red balls and 3 blue balls. If two balls are drawn at random from the bag, what is the probability that both the balls are red? Answer: Total number of ways of drawing 2 balls from the bag = 8C2 = 28 (using the combination formula). Number of ways of drawing 2 red balls from the bag = 5C2 = 10. So, the probability of drawing 2 red balls = 10/28 = 5/14.
- A letter is chosen at random from the English alphabet. What is the probability that the letter chosen is a consonant? Answer: There are 21 consonants in the English alphabet (excluding the letter ‘y’). Total number of letters in the English alphabet = 26. So, the probability of choosing a consonant = 21/26.

**CBSE Class 10 Maths Important Questions Answers MCQs Chapter 15 Probability**

A bag contains 5 red balls, 3 green balls, and 2 blue balls. If a ball is drawn at random from the bag, what is the probability of getting a green or blue ball?

a) 1/2

b) 5/10

c) 3/10

d) 5/9

Answer: c) 3/10

A coin is tossed 4 times. What is the probability of getting exactly 3 heads?

a) 1/2

b) 1/8

c) 1/16

d) 1/4

Answer: b) 1/8

In a class of 40 students, 15 play cricket, 20 play football, and 5 play both cricket and football. What is the probability of a student chosen at random playing either cricket or football?

a) 7/10

b) 2/3

c) 3/4

d) 3/8

Answer: a) 7/10

A box contains 8 red balls and 6 blue balls. If 3 balls are drawn at random without replacement, what is the probability of getting 2 red balls and 1 blue ball in any order?

a) 15/28

b) 12/33

c) 8/21

d) 1/3

Answer: a) 15/28

A deck of 52 playing cards is shuffled and one card is drawn at random. What is the probability of getting a heart or a face card?

a) 5/13

b) 17/52

c) 5/16

d) 9/52

Answer: c) 5/16

## CBSE Class 10 Maths Notes Chapter 15 Probability

**Probability:** It is the numerical measurement of the degree of certainty.

- The theoretical probability associated with an event E is defined as “If there are ‘n’ elementary events associated with a random experiment and m of these are favourable to the event E then the probability of occurrence of an event is defined by P(E) as the ratio mn “.
- If P(E) = 1, then it is called a ‘Certain Event’.
- If P(E) = 0, then it is called an ‘Impossible Event’.
- The probability of an event E is a number P(E) such that: 0 ≤ P(E) ≤ 1
- An event having only one outcome is called an elementary event. The sum of the probabilities of all the elementary events of an experiment is 1.
- For any event E, P(E) + P(E¯) = 1, where E¯ stands for ‘not E’. E and E¯ is called complementary events.
- Favourable outcomes are those outcomes in the sample space that are favourable to the occurrence of an event.

**Sample Space**

A collection of all possible outcomes of an experiment is known as sample space. It is denoted by ‘S’ and represented in curly brackets.**Examples of Sample Spaces:**

A coin is tossed = Event

E_{1} = Getting a head (H) on the upper face

E_{2} = Getting a tail (T) on the upper face

S = {H, T}

Total number of outcomes = 2

Two coins are tossed = Event = E

E_{1} = Getting a head on coin 1 and a tail on coin 2 = (H, T)

E_{2} = Getting a head on both coin 1 and coin 2 = (H, H)

E_{3} = Getting a tail on coin 1 and a head on coin 2 = (T, H)

E_{4} = Getting a tail on both, coin 1 and coin 2 = (T, T)

S = {(H, T), (H, H), (T, H), (T, T)}.

Total number of outcomes = 4

**NOTE:** In probability the order in which events occur is important

E_{1} & E_{3} are treated as different outcomes.

Important Tips

**Coin:**A coin has two faces termed a Head and Tail.**Dice:**A dice is a small cube that has between one to six spots or numbers on its sides, which is used in games.**Cards:**A pack of playing cards consists of four suits called Hearts, Spades, Diamonds, and Clubs. Each suite consists of 13 cards.

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