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# RS Aggarwal Class 10 Chapter 19 Solutions (Probability)

RS Aggarwal Solutions for Class 10 Maths Chapter 19 ‘Probability’ should be referred to any time you have doubts in the chapter. This chapter gives a good basic knowledge of probability and builds on it to present more complex questions. In this chapter of RS Aggarwal Class 10 Maths Solutions, you will study various terms and formulas related to probability such as random experiment, and possible outcomes, events, sample, space, fundamentals of probability and its properties, sure and impossible events, and complimentary events.

There are 3 exercises with a total of 97 questions in the chapter. There are many word problems and real-life problems to give a wide range of questions. Questions have mostly short and long answers and there is a section with objective type questions as well in this chapter. RS Aggarwal books have questions formulated on CBSE curriculum and guidelines hence practising with them will give you ample experience on questions which are exam-oriented. You can be sure that you have covered all areas that might appear in boards or competitive exams.

Probability is interesting as well as a little tricky concept. Our experienced faculty has in-depth knowledge of this topic to provide you with accurate solutions that are extremely easy to follow. Our solutions for RS Aggarwal Class 10 Maths Chapter 19 can be accessed easily from anywhere. We explain the fundamentals behind each topic so that you are equipped with the knowledge to tackle all kinds of questions related to this chapter.

## Important Topics for RS Aggarwal Solutions for Class 10 Chapter 19: Probability

Arab mathematicians were the first who attempted to give a numerical value to the probability of events. Gerolamo Cardano in the sixteenth century, and then Pierre de Fermat and Blaise Pascal in the seventeenth century enhanced this further with modern methods. Their experiments like “problem of coins” and “throwing of die” brought about many ways of presenting this concept.

Simply put probability is a number of possible outcomes of any event.  Before we delve into formulas, let us look at some commonly used terms in 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 which has numbers 1-6 on its 6 sides.
• Cards – A deck of cards has 52 cards in it with 4 suits. There are 26 red cards and 26 black ones. The 2 red suits are diamonds and hearts with 13 cards in each suit. The 2 black suits are spade and clubs with 13 cards in each of them also. The 13 cards range from A – 10 then Joker, Queen, and King.
• Random Experiment and Trial–. In this topic, you learn about what is the difference between an experiment and a trial. Any action which produces well-defined outcomes, which are 2 or more in number, is termed as an “experiment”. A “random experiment” is the one in which all possible outcomes are known but the exact outcome cannot be predicted in advance. An experiment can be repeated an infinite number of times and a single experiment out of these repetitions is called a “trial”. For Example, tossing a coin has 2 possible outcomes, head or tail; picking a card from a deck of cards has 52 possible outcomes.
• Sample Space – Sample space is a set that depicts all possible outcomes of an event and “point” is a single element of the sample space. For example, in the case of tossing 2 coins, its sample space can be represented as {(H, H), (H, T), (T, H), (T, T)}
• Probability – When we numerically measure the likelihood of an event in a trial, it gives us its probability. Probability is always a chance of that event of occurring, not a definite possibility. Probability ranges from 0 to 1. It is given by:

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

Here P(E) is the empirical probability of an event happening and n is the total number of trials.

One must understand the following to master probability sums:

• In any experiment what is the total number of possible outcomes
• In any experiment what is the total number of favourable events
• Event – Understanding what events are and different kinds of events are important to solve the problems. Any experiment results in events. An event can be described as a subset of sample space. For example, sample space of throwing a dice would be S = {1, 2, 3, 4, 5, 6} and an event is a subset of this S, so {1, 2, 3) or {4, 5, 6} are all events.
• Favourable event – If the event we expect happens in a trial then that’s a favourable event.
• Unfavourable event– When the event we expect does not occur in a trial, it is called an unfavourable event.
• The sum of all favourable and unfavourable events is the well-defined set of outcomes
• It can be concluded that if in a sample space S, there are n favourable events then there are S – n number of unfavourable outcomes.
• The number of trials determines the probability of a favourable or unfavourable event. 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.
• Impossible event – An event that will never occur in any trial is an impossible event. It is denoted by a null set (Φ). For example, when you throw a die, the occurrence of number 7 is an impossible event since a die has only numbered 1-6 on its sides.
• Sure event – If the probability of an event in a trial is 1 then it is a sure event. For example, when you throw a die, the probability of getting a number >=1 is 1, so it is a sure event.
• 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 E’ (not E)

P(E) + P(E’) = 1, where 0 <= P(E) <= 1

• Equally likely events – If the probability of any event in a trial is 50% or ½, then that is an equally likely event. For example, when we toss an unbiased coin, the probability of getting a head is ½.

### Exercise Discussions of RS Aggarwal Solutions for Class 10 Chapter 19: Probability

Exercise 19A

It has 35 questions which are a mix of fill in the blanks and short answer types. You would need to use some of the definitions learned, formulas for probability on different kinds of experiments like the tossing of a coin or throwing or dying or picking up a card from a deck of cards. Some questions are on complementary events and you would learn how to form sample space for any random experiment.

Exercise 19B

In this exercise, questions revolve around cards, tickets, and a few other common events. You need to give short to long answer types for these 25 questions in this set.

Exercise 19C

This exercise includes multiple-choice questions where you need to choose one correct answer from given choices. There are a total of 37 questions that test you on all the concepts of probability along with the formulas, definitions learned in the chapter.

### Benefits of RS Aggarwal Solutions for Class 10 Chapter 19: Probability by Instasolv

• Probability is a crucial topic that can help you score good marks in Class 10 board exams and also other competitive exams.
• You might sometimes find yourself struggling with some of these concepts hence it is sometimes necessary to equip yourself with material like we provide to have a better understanding of this topic.

This time-consuming topic can be learned quickly by following the methods applied by our team of experts in the Class 10 RS Aggarwal Solutions for Chapter 19.

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