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Business Mathematics and Basic Statistics · Class 11 Commerce

Ch 11Introduction to Probability — Class 11 Business Mathematics and Basic Statistics, concept-first.

In everyday life we constantly meet processes whose exact result cannot be predicted in advance, even though every result that COULD occur is already known beforehand — tossing a coin, rolling a die, or drawing a card from a well-shuffled deck are all examples.

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Concepts

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Key concepts

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Simple, Compound, Mutually Exclusive and Collectively Exhaustive Events

An event is any subset of . A simple event has exactly one sample point; a compound event has two or more. Two or more events are mutually exclusive if their intersection is empty (cannot occur together), and collectivel…

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

1

Random Experiment and Sample Space

In everyday life we constantly meet processes whose exact result cannot be predicted in advance, even though every result that COULD occur is already known beforehand — tossing a coin, rolling a die,…

2

Events — Simple and Compound

An event is any subset of the sample space — that is, any collection of outcomes we are specifically interested in.

3

Mutually Exclusive and Collectively Exhaustive Events

Two or more events are called mutually exclusive if they cannot occur together in a single performance of the experiment — that is, no sample point is common to any two of them.

4

Equally Likely Events and Sample-Point Counting

The outcomes of a random experiment are called equally likely when every individual outcome has exactly the same chance of occurring as every other outcome — no outcome is favoured over any other.

5

Classical Definition of Probability

When the sample space of a random experiment consists of a finite number of equally likely outcomes, the classical (mathematical) definition of probability of an event is:

Exercises

+Show 6 questions6 questions
  1. Q7Two fair coins are tossed together. Let $A = $ 'getting at least one head' and $B = $ 'getting no head'. Examine whether $A$ and $B$ are mut…Free
  2. Q8A coin is known to be biased so that it lands Heads 70% of the time and Tails 30% of the time. Can the two outcomes $\{H, T\}$ of a single t…Free
  3. Q9A fair die is rolled once. Find the probability of getting a number greater than 4.Preview
  4. Q10A card is drawn at random from a well-shuffled deck of 52 playing cards. Find the probability that it is (i) a king, (ii) a red card, (iii)…Preview
  5. Q11Two fair dice are rolled together. Find $n(S)$ and the probability that the sum of the numbers shown on the two dice is 7.Preview
  6. Q12Three fair coins are tossed simultaneously. Find the probability of getting exactly two heads.Preview

More questions

+Show 6 questions6 questions
  1. Example 1Write the sample space when a single fair coin is tossed once, and state $n(S)$.Free
  2. Example 2Two fair coins are tossed simultaneously. Write the sample space and find $n(S)$. Also write the event 'getting exactly one head' as a set,…Free
  3. Example 3A fair die is rolled once. Write the sample space. Classify the event 'getting a 4' and the event 'getting an even number' as simple or comp…Preview
  4. Example 4A coin is tossed and a die is rolled together. Using the multiplication principle, find $n(S)$, and write the sample space.Preview
  5. Example 5A card is drawn at random from a well-shuffled deck of 52 playing cards. Classify each of the following as a simple or compound event: (i) d…Preview
  6. Example 6On a single roll of a fair die, let $E_1 = $ 'getting an even number' and $E_2 = $ 'getting an odd number'. Examine whether $E_1$ and $E_2$…Preview