Probability formula properties and solved examples for Class 10 exams
Get ready to increase your Maths board exam score with Vedantu’s probability class 10 notes. You can use the expert solutions given at Vedantu in order to learn how you would find the number of colored balls in a bag and much more? Or after understanding the concept of probability, you can also prove that a given event will be an impossible event.
So, let us understand how to use the probability formula with which you can find answers based on the information about the number of favorable outcomes along with the total number of outcomes.
NCERT Class 10 Probability Revision Notes At Vedantu
Revise your probability concepts to improve your exam score with our NCERT class 10 probability topic notes and other resources.
Probability Class 10 Important Questions PDF
This PDF on Probability Problems for Class 10 CBSE is created as per the latest syllabus. Here in the following downloadable PDF, we have covered everything related to Probability Class 10. Also, there are solved step-by-step examples which you can have a look at for your better understanding. So, with our probability class 10 important questions PDF, you can have a clear idea of the topic and should be able to get high marks in Class 10 Mathematics CBSE Board exams.
Formula for Solving Probability Problems for Class 10 CBSE
In the general formula of probability:
P(A) means 'the probability of A' where A is an event we are interested in,
P(A|B) stands for 'the probability of A given that B occurs', and
P( A0) stands for 'the probability of A0 ', or it tells about 'the probability that A does not take place.’
The Rules Of Probability
Probability has its own set of rules that are used in solving both simple and complex probability problems. So, here are three most widely used rules of probability.
Rule 1: The Addition rule
Rule 2: The Multiplication rule
Rule 3: The Complement rule
1. The Addition Rule
The representation for this rule is as follows:
P(A or B) = P(A) + P(B) - P(A and B)
If there are two events A and B which are mutually exclusive of each other or the two events which can’t take place together, then the third term is 0. That means, the rule can then be reduced to:
P(A or B) = P(A) + P(B)
2. The Multiplication Rule
The formula for this rule is:
P(A and B) = P(B) * P(A | B) or P(A) * P(B|A)
In this rule, both the events A and B are independent events. The formula can also be reduced to P(A and B) = P(A) * P(B). However, this rule states that each event out of these 2 events is not affected by the outcome of the other event.
Consider the coin toss. If the first result came as a head then also there is no guarantee that in the next toss the result will be tails. So, the probability is 0.25 or 25% that it can be heads again or tails. Are you wondering how it's 25%? Let's have a look at the calculations.
P = P(heads) * P(tails) = (0.5) * (0.5) = 0.25
3. The Complement Rule
Here is its representation…
P(not A) = 1 - P(A)
Here, the two events, A and B can never take place together but one event out of these two will always take place. For instance, if the weatherman says that there’s a 40% chance of rain tomorrow then the chances of no rain are
40% = 0.4
P(no rain) = 1 - P(rain) = 1 - 0.4 = 0.6/ 60%.
FAQs on Probability for Class 10 Complete Guide with Concepts and Practice
1. What is probability in Class 10 Maths?
Probability is the measure of the chance of an event occurring and is given by the formula Probability = (Number of favourable outcomes) / (Total number of possible outcomes). In Class 10 Maths, probability deals with experiments like tossing a coin, rolling a dice, or drawing a card. The value of probability always lies between 0 and 1, where 0 means an impossible event and 1 means a sure event.
2. What is the formula for probability in Class 10?
The basic formula for probability is P(E) = n(E) / n(S), where n(E) is the number of favourable outcomes and n(S) is the total number of possible outcomes. Here:
- P(E) = Probability of event E
- n(E) = Number of outcomes favourable to E
- n(S) = Total outcomes in the sample space
3. What is a sample space in probability?
A sample space is the set of all possible outcomes of a random experiment and is denoted by S. For example:
- When tossing a coin, S = {H, T}
- When rolling a dice, S = {1, 2, 3, 4, 5, 6}
4. What is the probability of getting a head when a coin is tossed?
The probability of getting a head when a fair coin is tossed is 1/2. The sample space is {H, T}, so total outcomes = 2. Number of favourable outcomes (Head) = 1. Using the formula P(E) = n(E)/n(S), we get P(H) = 1/2.
5. What is the probability of getting a number less than 3 on a dice?
The probability of getting a number less than 3 on a fair dice is 2/6 = 1/3. The sample space is {1, 2, 3, 4, 5, 6}. Numbers less than 3 are {1, 2}, so favourable outcomes = 2 and total outcomes = 6. Therefore, P(E) = 2/6 = 1/3.
6. What is the difference between theoretical probability and experimental probability?
Theoretical probability is calculated using a formula, while experimental probability is based on actual experiments or observations.
- Theoretical probability: Uses P(E) = n(E)/n(S)
- Experimental probability: Uses Number of times event occurs / Total number of trials
7. What are complementary events in probability?
Complementary events are two events whose probabilities add up to 1. If A is an event, then its complement is denoted by A̅. The formula is P(A) + P(A̅) = 1. For example, probability of getting a head and not getting a head when tossing a coin are complementary events.
8. What is the probability of an impossible event?
The probability of an impossible event is 0. An impossible event is one that cannot happen in any situation. For example, getting a number 7 when rolling a standard six-faced dice is impossible, so P(7) = 0.
9. What is the probability of a sure event?
The probability of a sure event is 1. A sure event is one that will definitely occur. For example, when rolling a dice, getting a number less than 7 is certain because all outcomes (1–6) satisfy it, so P(E) = 6/6 = 1.
10. How do you find probability step by step in Class 10 Maths?
To find probability in Class 10 Maths, use the formula P(E) = n(E)/n(S) and follow these steps:
- Step 1: Write the sample space (S).
- Step 2: Count total outcomes n(S).
- Step 3: Identify favourable outcomes for event E.
- Step 4: Count favourable outcomes n(E).
- Step 5: Substitute into the formula and simplify.
