NCERT Books for Class 9 Maths Chapter 15

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Probability 

Probability denotes the likelihood of something happening. It's a field of mathematics that studies the probability of a random event occurring. From 0 to 1, the value is expressed. It is a mathematical concept that describes how likely it is that events will occur. Probability is defined as the degree to which something is likely to happen. This is the fundamental probability theory, which is also applied to the probability distribution, where you will learn about the possible results of a random experiment. To determine the likelihood of a particular event occurring, we must first determine the total number of alternative possibilities. Probabilities range from 0 to 1, with 0 indicating impossibility and 1 indicating certainty, generally. The probabilities of an event increasing mean it is more likely that it will happen.

Important Definitions of the Chapter 

Randomness: The Random Experiment occurs when we are performing an experiment and have no idea what the next result of the experiment will be.

Trial: A trial is an activity with several outcomes, rather than simply one. For instance, take the spade 7 cards from the deck of cards or the result of a dice roll, and so on.

Event: An event that occurs during the execution of an experiment is the collection of some of the experiment's outcomes. When we roll a dice, for example, the chances of getting an odd number are three, i.e. 1, 3, 5. As a result, the event would have three possible outcomes.

Impossible Events: If an event is not feasible to occur during a test, the chance of it occurring is zero (0). This is referred to as an "Impossible Event." You can't, for example, throw dice with the number eight as the outcome. As a result, obtaining an 8 on dice has a 0% chance of happening.

Sure or Certain event: It is stated to be a definite probability when a test shows that there is a certainty that an event will occur. The likelihood is 1 in this case. For example, drawing a red ball from a bag containing exclusively red balls is almost certain.

This illustrates that an event's probability can range between 1 and 0. Thus, 0 ≤ P (E) ≤ 1.

Sample Questions

There is just one exercise in Chapter 15 of the NCERT book for Class 9 Math. There are four long answer questions, three short answer questions, and three extremely long answer questions in this set. You will gain a strong understanding of the issue as you practise. Following are a few sample questions

1. In a cricket match, a batsman hits a boundary 6 times out of 30 balls she plays. Find the probability that he did not hit a boundary.

Answer:

According to the question,

Total number of balls = 30

Numbers of boundary = 6

Number of time batsman didn’t hit boundary = 30 – 6 = 24

Probability he did not hit a boundary = 24/30 = 4/5

2. Find the probability that a student is chosen at random

(i) likes statistics, (ii) does not like it.

Answer:

Total number of students = 135+65 = 200

(i) Number of students who like statistics = 135

, the probability that a student likes statistics = 135/200 = 27/40

(ii) Number of students who do not like statistics = 65

The probability that a student does not like statistics = 65/200 = 13/40

3. Note the frequency of two-wheelers, three-wheelers and four-wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler.

Answer:

The question is an activity to be performed by the students.

Hence, perform the activity by yourself and note down your inference.

4. Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by 3? Remember that a number is divisible by 3 if the sum of its digits is divisible by 3.

Answer:

The question is an activity to be performed by the students.

Hence, perform the activity by yourself and note down your inference.

5. Eleven bags of rice, each marked 5 kg, actually contained the following weights of rice (in kg):

4.97  5.05  5.08 5.03 5.00 5.06 5.08      4.98   5.04   5.07   5.00

Find the probability that any of these bags chosen at random contains more than 5 kg of rice.

Answer:

Total number of bags present = 11

Number of bags containing more than 5 kg of rice = 7

The probability that any of the bags chosen at random contains more than 5 kg of rice= 7/11.