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# RS Aggarwal Class 9 Chapter 19 Solutions (Probability)

RS Aggarwal Solutions for Class 9 Maths Chapter 19 braces students with knowledge on how to deal with probability related questions. Probability is an important chapter of RS Aggarwal Class 9 Maths Solutions that increase in complexity as you reach higher classes and you always get questions from this topic in CBSE or entrance exams. You might find some of the concepts of Probability a little tough to crack. So it becomes mandatory sometimes to get help in understanding the fundamentals and forming a strong base in this topic.

This chapter begins by giving you a brief history of probability along with some important terms and formulas used in probability. You also get to practice some of the operations related to probability and learn about their outcomes. This chapter has 1 exercise with a total of 18 questions which are a mix of short answers and fill in the blanks type questions which give you ample exposure and practice to any kind of question which you might need to solve in exams.

Our experts with years of experience in the education department understand how a solution to a problem is to be provided so as to allow you to widen your approach towards solving problems. We strive to stimulate a higher level of thinking so that you can rest assured of handling all sorts of problems during exams without any stress.

## Important Topics for RS Aggarwal Solutions for Class 9 Chapter 19: Probability

Probability is part of our everyday life where any uncertain event is termed as “probable”. The attempt to measure this uncertainty was first done by Arab mathematicians but modern theories like “problem of coins” came from works of Gerolamo Cardano in the sixteenth century, and by Pierre de Fermat and Blaise Pascal in the seventeenth century. Let us take a look at some of the important terms and definitions of Probability:

• Some common objects used in probability questions –
• Coin – A coin has 2 faces, head, and tail.
• Dice or Die – A dice is a cube having 6 faces with 6 different numbers on it (1 – 6)
• Cards – A deck of cards has 52 cards with 26 red and 26 black coloured ones. It has 4 suits with 13 cards in each suit, clubs, diamonds, hearts, and spades. The 13 cards range from A – 10, Joker, King, and Queen.
• Experiment – Any action which results in 2 or more outcomes is termed as an experiment. An experiment can be repeated an infinite number of times.

E.g. Tossing a coin has 2 possible outcomes, head or tail; picking a card from a deck of cards has 52 possible outcomes.

• Sample Space – A set comprising of all possible outcomes of an event is termed as sample space. A single element of sample space is called a point.

E.g. – When you toss a coin, sample space ahs 2 points namely (H) or (T) which stand for heads or tails respectively.

• Event – Event is a subset of sample space. E.g: If we throw a dice, its sample space would be S = {1, 2, 3, 4, 5, 6} and an event can be anything that belongs to S, so {1, 2, 5) or {3, 2, 6} are all events.
• A null set Φ and whole sample S itself are events. A null set is an impossible event.
• Probability – The likelihood of an event to occur, when measured numerically, is called its probability. It is not a definite occurrence but predicts how much the chance of that event to occur is. It has a range from 0 – 1, 0 means no probability and 1 means 100% chance.

P (E) = number of trials in which an event happened / n

Here P (E) – the empirical probability of an event happening

n – Total number of trials.

• Favourable event – In a trial when the expected event happens it is called a favourable event.
• Unfavourable event– When the expected event does not occur, it is called an unfavourable event.
• The sum of all favourable and unfavourable events is the well-defined set of outcomes
• If in a sample space S, an event has n number of favourable outcomes then it has S – n number of unfavourable outcomes.
• The probability of a favourable or unfavourable event depends on the number of trials and the sum of these probabilities is always 1 i.e.

Probability of the occurrence of an event + Probability of the non-occurrence of that event = 1.

• Complimentary event – If an event E1 occurs only if event E does not occur then E1 is called the complementary event of E. It has a notation (not E)

P(E) + P(not E) = 1

where 0 <= P(E) <= 1

### Exercise Discussions of RS Aggarwal Solutions for Class 9, Chapter 19: Probability

This chapter has a single exercise with 18 questions. These questions would help you hone your expertise on finding the probability of events that involve one or more coins tossing, throwing of dice, finding probability based on the frequency distribution.

### Benefits of RS Aggarwal Solutions for Class 9, Chapter 19: Probability

• The chapter-wise solutions provided for our team of experts will help you understand the many ways and methods that can be applied to solve any problem.
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