Higher Algebra Hall & Knight Probability (Chapter 32) Solutions
Hall and Knight Higher Algebra Solutions for Chapter 32 ‘Probability’ have been formulated to help you with the complex exercise questions in this chapter. These solutions are prepared as per the latest guidelines for JEE and NEET syllabus by our subject matter experts. You will learn some crucial definitions and illustrations, compound events, and the probability of two events that will happen. You will also get into the discussion of the formula that holds for the dependent events, the chance of occurrence of mutually exclusive ways in which the event happens. Other important topics include Inverse probability, statement of Bernoulli’s theorem, concurrent testimony, traditional testimony, and local probability.
In this chapter of Higher Algebra book by Hall & Knight, there are 109 questions compiled in a total of 5 exercises. The questions are arranged topic-wise while the last exercise comprises miscellaneous questions based on all the concepts. The exercise questions in this chapter are majorly word problems where you will learn to find the probability of an event that took place ‘r’ times in ‘n’ number of trials. Solving these questions will help you understand the pattern of frequently asked questions in the competitive exams such as the IIT Joint Entrance Exam, BITSAT, etc. We recommend that you solve these questions in a detailed manner.
The team of experienced Maths teachers at Instasolv has covered each topic in this chapter through the Higher Algebra By H.S. Hall and S.R. Knight solutions for all exercise questions. To understand Probability, it is important to be able to infer the data from a compound event. Such complex topics have been made easy for you in a step by step fashion. You will find assistance at every step with precise reasoning. The solutions to Elementary Algebra and Higher Algebra by Hall & Knight book have been written in a format strictly compliant to the latest competitive exam guidelines for JEE and NEET.
Important Topics Covered under Hall and Knight Higher Algebra Solutions Chapter 32: Probability
If we assume an event that can occur in ‘a’ ways and can fail in ‘b’ ways, such that each of these ways is equally likely, then the probability of the occurrence of the event is given as and that the event will fail is given by
It should be noted that if the probability of occurrence of a given event is p, then the probability that the even will fail is equivalent to 1-p.
can also be read as the odds are ‘a’ to ‘b’ in favour of the even, or ‘b’ to ‘a’ against the event.
When there is an amalgamation of two or more simple events in an event, then this joint occurrence of events is termed as a Compound Event.
This can be explained with the help of an example. Suppose there is a bag comprising 5 black and 5 blue balls and the balls are drawn out of it twice, successively. To calculate that the first three balls drawn are black or blue, we will regard this event as a compound event.
Dependent and Independent Events
- An event is dependent or independent as per the occurrence of one does or does not affect the occurrence of others respectively. We also term the dependent events as contingent events.
- To find the probability of two independent events together, the probabilities of which are known, we use the following formulae:
Assuming that the first event will occur in ‘a’ ways and fail in ‘b’ ways and the second event will occur in a’ ways and fail in b’ ways, and all the events are equally likely then we can associate a+b cases with a’+b’ cases to form (a+b)(a’+b’) compound cases which are equally likely to occur,
- The chance that both events will happen
- The chance that both will fail
- First will occur and second, will fail,
- First will fail and the second event will occur,
Consider p as the probability that an event will occur in a single trial and if we increase the number of trials indefinitely, then it becomes certain that the limit of the ratio of the number of successes to the number of trials is p, that is, if the number of trials is N, the number of successes is given as pN.
Exercise Discussion of Hall and Knight Higher Algebra Solutions Chapter 32: Probability
- Exercise 32.a consists of questions based on the basic definitions of probability and compound events.
- Exercise 32.b consists of questions based on the formula that holds true for the dependent events, the chance of occurrence of mutually exclusive ways in which the event happens
- The topics covered in exercise 32.c are based on the evaluation of the probability of an event that took placer times in n number of trials.
- The questions in exercise 32.d are based on inverse probability, statement of Bernoulli’s theorem, concurrent testimony, and traditional testimony
- Exercise 32.e comprises 35 word-problems which are complex in nature and include questions based on all the topics of probability learnt in this chapter so far such as local probability.
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