NCERT 9th Standard : Prabability

Chapter 15 - Probability

The extent to which an event is likely to occur measured by the ratio of the favorable cases to the whole number of possible cases. The higher number of probability of an event, the more likely it is that the event will occur.

In everyday life, we come across statements such as

(1) It will probably rain today.

(2) I doubt that he will pass the test.

(3) Most probably, Kavita will stand first in the annual examination.

(4) Chances are high that the prices of diesel will go up.

(5) There is a 50-50 chance of India winning a toss in today’s match.

The words ‘probably’, ‘doubt’, ‘most probably’, ‘chances’, etc., used in the statements above involve an element of uncertainty. For example, in (1), ‘probably rain’ will mean it may rain or may not rain today. We are predicting rain today based on our past experience when it rained under similar conditions. Similar predictions are also made in other cases listed in (2) to (5).

Some Important Points:

Coin: Coin has two faces. They are called Head & Tail.

Die (Dice): Die is a solid in the form of cube, having six faces.

Cards: A pack of cards has 52 cards out of which 26 are RED cards & 26 are BLACK cards.

        I.            26 red cards contain 13 cards of diamond ♦ and 13 cards of heart ♥.

      II.            26 black cards contain 13 cards spade ♠ and 13 cards of club ♣.

    III.            13 cards are 1(ace), 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, & King.

    IV.            Card have 1 is also called an ACE.

Probability: An experiment approach

A trail is an action which results in one or several outcomes. An event for an experiment is the collect of some outcomes of the experiment.

Let ‘n’ be the total number of trial. The probability of an event E happening is given by,

NOTES:

The Probability of an event lies between 0 and 1. (It can be any fraction number between 0 & 1).

The sum of probabilities of all the possible outcomes of a trial is 1.

Probability of occurrence of an event + Probability of non-occurrence of an event = 1

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