Mathematics is the foundation of almost all the objects that we see or experience around us such as circles; probability and geometry. We come across a number of scenarios in daily life that require us to use the concept of probability, such as “Will it rain today?” or “What are the chances of India winning the next match?”. So if you are studying in class 9 and want to gain a better understanding of the concepts of probability, this blog covers all details about Class 9 Probability.
Also Read: CBSE Class 9 Maths Syllabus
This Blog Includes:
Introduction to Probability
Let us begin with understanding the basics of Class 9 probability. In very simple words, Probability is the measure of the likelihood of occurrence of an event. For example – if we toss a coin, the chance of getting a head is 50% or we can say the probability of getting a head is 50%.
Majority of the events cannot be predicted with certainty, but we can calculate the likelihood of the event i.e., how likely it is that the event will occur and that is known as Probability.
The probability of an event can be anything between 0 to 1, where 0 and 1 are the extremes. 0 means that the event cannot occur and 1 means that the event will occur for certain.
Must Read: NCERT Solution of Maths Class 9
Let us go through some important terms in class 9 Probability –
To understand class 9 probability properly, it is important to understand the concept of experiment. In layman terms, an experiment is a procedure which can be repeated again and again or a set of actions which have well-defined possible outcomes. It may have on or more outcomes. It is also commonly known as the Sample Space which is denoted by ‘S’ i.e., it is a collection of all the possible outcomes. For example – tossing a coin is an experiment, it can be repeated again and again and has only two outcomes – Head or Tail, so the Sample Space will be (Head, Tail)
Trial is also an important part in the chapter of class 9 probability. A trial is a single event which is undertaken in order to determine the outcome, we calculate probabilities of individual trials. When we take all possible events together, we get the sample space or experiment. For example – tossing a coin once is a trial.
Also Read: Circles Class 9 Study Notes
Experimental probability is based on real observations and sufficient records of the occurrence of events, also known as empirical probability. A series of actual tests are performed to determine the frequency of some incident. Random experiments are defined as experiments which do not have a predetermined outcome. To assess their chance, random experiments are replicated several times. An experiment is repeated a set number of times and is regarded as a trial for each iteration. Mathematically, the experimental probability formula is defined by:
P(E) = Number of Favourable Outcomes/Total number of outcomes
When we perform a trial, two things are possible – it will be a favorable event or an unfavorable event. But what is a favorable or unfavorable event?
- When we are performing a trial for an expected outcome and we get the expected outcome, it is called a favorable event. However, if we do not get the expected outcome, it is called an unfavorable event.
- Example: We are performing a trial of tossing a coin to get head, so if we get head, it will be a favorable event, but if we get tail, it is an unfavorable event.
- Sum of favorable events and unfavorable events gives us the Sample Space, in other words, if in a Sample Space (S), there are ‘n’ favorable outcomes, then there will be ‘S-n’ unfavorable outcomes.
- The probability for either favorable or unfavorable events depends on the number of trials done. However, the sum of these two probabilities will always be 1.
Explore: Class 9 Quadrilaterals Study Notes
Two of the most common experiments while explaining probability are –
- Coin tossing experiment
- Dice rolling experiment
Coin Tossing Experiment
We start with a fair coin and toss it, now there are only two outcomes possible – Heads or Tails. So, if our event of interest is getting a head, we calculate the probability as follows –
Total number of outcomes – 2
Number of outcomes to get head – 1
P (getting a head) = Number of outcomes to get head
Total number of outcomes= 12
Dice Rolling Experiment
When we roll a dice, we can get any number between 1 to 6, so let our event of interest be getting a 3, we calculate the probability as follows –
Total number of outcomes – 6
Number of outcomes to get 3 – 1
P (getting a 3) = Number of outcomes to get 3
Total number of outcomes=16
Also Read: Statistics Class 9 Maths Study Notes
Go through these practice questions to revise the chapter on class 9 Probability throughly.
- Find out the probability of the occurrence of an event if the probability of the event occurring is 0.46.
- 10 cards are picked out of order and shuffled further. The cards are: 9,5,4,2,6,8,2,3,7,8. What is the probability of picking a card which is more than 5?
- 92 workers are married out of 200 workers in a factory. What will be the probability of selecting a worker who is unmarried?
- A bag is full of black and red balls. The probability of picking a red ball is x/2. Find the value of x if the probability of picking the black ball is 3/4.
- Aman tossed a coin 120 times and found that Heads comes 1 1 1 1 5 times and tails comes 34 times. If a coin is tossed randomly what is the probability of getting (a). A Tail, (b) Heads
We hope that this blog has helped you understand the basics of class 9 probability. If you want to learn more or want an insight into various subjects such as Class 9 Chemistry, Biology, English, Physics, please refer to our extensive study notes. For any career-related guidance, contact the experts at Leverage Edu and take a step forward on your path to excellence. Sign up for a free session today!