‘रचना-प्रयोग’ का मुख्य उद्देश्य क्या है?

व्याकरण का व्यावहारिक प्रयोग सिखाना

‘द्वितीयः’ किस प्रकार की संख्या है?

क्रमवाचक (दूसरा)

What is the probability of a sure event and an impossible event?

\(1\) for a sure event and \(0\) for an impossible event.

If \(P(E) = 0.3\), what is \(P(\text{not }E)\)?

\(P(\text{not }E) = 1 - 0.3 = 0.7\).

Write the formula for the theoretical probability of an event E.

\(P(E) = \dfrac{\text{number of outcomes favourable to } E}{\text{total number of equally likely outcomes}}\).

What is the probability of a sure event and of an impossible event?

\(1\) for a sure (certain) event and \(0\) for an impossible event.

What is the range of the probability of any event?

The probability of any event lies between 0 and 1, that is \(0 \le P(E) \le 1\).

What are complementary events, and how are their probabilities related?

An event \(E\) and "not \(E\)" are complementary; \(P(E) + P(\text{not }E) = 1\), so \(P(\text{not }E) = 1 - P(E)\).

A die is thrown once. What is the probability of getting an even number?

Favourable outcomes are 2, 4, 6 (three of them) out of six, so \(P = \dfrac{3}{6} = \dfrac{1}{2}\).

A card is drawn from a well-shuffled pack of 52. What is the probability that it is a king?

There are 4 kings, so \(P(\text{king}) = \dfrac{4}{52} = \dfrac{1}{13}\).

Two coins are tossed together. What is the probability of getting two heads?

The outcomes are HH, HT, TH, TT; only one is favourable, so \(P(\text{two heads}) = \dfrac{1}{4}\).

If the probability of an event is 0.7, what is the probability of its not happening?

\(P(\text{not }E) = 1 - 0.7 = 0.3\).

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Chapter 14: ProbabilityClass 10 Mathematics — summary, notes, extra questions & NCERT solutions

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The theoretical probability of an event E is:

Summary

Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain). This chapter develops the theoretical (classical) definition: the probability of an event equals the number of favourable outcomes divided by the total number of equally likely outcomes. It applies this to everyday experiments such as tossing coins, rolling dice and drawing cards, and uses the fact that the probabilities of an event and its complement add up to 1. Probability provides a precise language for reasoning about chance and uncertainty.

Theoretical probabilitySimple experiments (coins, dice, cards)Complementary events

Key terms

Probability of an event

\(P(E) = \dfrac{\text{favourable outcomes}}{\text{total outcomes}}\).

Sure/impossible event

Probability 1 (certain) or 0 (impossible).

Complementary event

\(P(\text{not }E) = 1 - P(E)\).

Equally likely outcomes

Outcomes that each have the same chance of occurring.

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EXERCISE 14.1

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Probability of an event

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\(P(E) = \dfrac{\text{favourable outcomes}}{\text{total outcomes}}\).

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