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Probability Class 10 Notes
Probability is a branch of mathematics that deals with the likelihood of an event occurring. In other words, it calculates the odds of something happening. Probability is expressed as a fraction, decimal, or percentage.
There are three basic steps to calculating Probability:
1. Identify the event you are trying to calculate the probability for.
2. Determine the possible outcomes of the event.
3. Calculate the probability of each outcome occurring.
Let’s take a look at an example:
You are playing a game of chance in which you have a choice of three different envelopes. One envelope contains a $100 bill, one envelope contains a $10 bill, and one envelope contains a $1 bill. You choose an envelope at random and find that it contains a $1 bill. What is the probability that the envelope you chose contained a $100 bill?
To calculate the probability of the event occurring, we first need to identify the event and determine the possible outcomes. In this case, the event is that the envelope chosen contains a $100 bill. The possible outcomes are that the envelope contains a $100 bill, a $10 bill, or a $1 bill.
Next, we need to calculate the probability of each outcome occurring. To do this, we use the following equation:
P(A) = (Number of outcomes that result in event A)/(Total number of outcomes
NCERT Class 10 Probability Revision Notes At Vedantu
, we understand that revision is an important step before the final exam. So, we provide you with NCERT Class 10 Probability revision notes. These revision notes will help you in understanding all the important concepts of Probability and also help you in clearing all your doubts.
1. Probability:
It is a numerical measure of the chance that an event will occur.
2. Probability of an event:
The probability of an event is the ratio of the number of favourable outcomes to the total number of outcomes.
3. Favourable outcomes:
These are the outcomes that are favourable to the event.
4. Total number of outcomes:
This is the number of all possible outcomes, favourable as well as unfavourable.
5. Probability of an event not happening:
This is the probability of an event not occurring. It is the ratio of the number of unfavourable outcomes to the total number of outcomes.
6. Odds:
The odds of an event are the ratio of the number of favourable outcomes to the number of unfavourable outcomes.
7. Odds against an event:
The odds against an event are the odds of an event not occurring.
8. Probability of an event occurring:
This is the probability of an event occurring. It is the ratio of the number of favourable outcomes to the total number of outcomes.
Probability Class 10 Important Questions PDF
1. What is a probability?
A probability is a number between 0 and 1 that expresses the likelihood that an event will occur.
2. What are the different types of probabilities?
There are three types of probabilities: empirical, theoretical, and subjective.
3. What is an empirical probability?
An empirical probability is a probability based on actual experience.
4. What is a theoretical probability?
A theoretical probability is a probability based on theoretical considerations.
5. What is a subjective probability?
A subjective probability is a probability based on personal opinion.
6. What is the difference between a probability and a percentage?
A probability is a number between 0 and 1 that expresses the likelihood that an event will occur. A percentage is a number between 0 and 100 that expresses the percentage of occurrence of an event.
7. What is the difference between a probability and a frequency?
A probability is a number between 0 and 1 that expresses the likelihood that an event will occur. A frequency is the number of times an event occurs in a given number of trials.
8. What is the difference between a probability and a percentage chance?
A probability is a number between 0 and 1 that expresses the likelihood that an event will occur. A percentage chance is a percentage that indicates the likelihood of an event occurring.
9. What is the difference between a probability and a
Formula for Solving Probability Problems for Class 10 CBSE
Let A denote the event that a randomly selected student is male, and B denote the event that a randomly selected student is a senior.
The probability that a randomly selected student is male and a senior is
P(A and B) = P(A)P(B)
The Rules Of Probability
There are a few key rules of probability that you need to remember in order to calculate probabilities accurately.
The Addition Rule
The addition rule states that the probability of two or more events happening is the sum of the individual probabilities of each event.
For example, if you want to calculate the probability of both rolling a 6 and rolling a 3 on two separate dice, you would use the addition rule to add the probabilities of each event happening.
The probability of rolling a 6 is 1/6 and the probability of rolling a 3 is 1/6, so the probability of rolling a 6 or a 3 is 1/6 + 1/6 = 2/6 = 1/3.
The Multiplication Rule
The multiplication rule states that the probability of two or more events happening is the product of the individual probabilities of each event.
For example, if you want to calculate the probability of both rolling a 6 and rolling a 2 on two separate dice, you would use the multiplication rule to multiply the probabilities of each event happening.
The probability of rolling a 6 is 1/6 and the probability of rolling a 2 is 1/6, so the probability of rolling a 6 or a 2 is 1/6 x 1/6 = 1/36.
1. The Addition Rule
The addition rule states that the derivative of a sum is the sum of the derivatives.
For example, if we have
f(x) = x2 + 3x
then
f'(x) = 2x + 3
2. The Multiplication Rule
The multiplication rule states that the probability of two independent events occurring is the product of their individual probabilities.
For example, if you roll a die, the probability of rolling a 3 is 1/6. If you then roll a second die, the probability of rolling a 3 is 1/6 again. Therefore, the probability of rolling two 3s is 1/6 * 1/6 = 1/36.
3. The Complement Rule
The complement rule states that the complement of a set is the set of all elements that are not in the set.
For example, the complement of {1, 2, 3} is {4, 5, 6}.
