9th Class Mathematics Probability

PROBABILITY

FUNDAMENTALS

• When the chance of occurring an event expressed quantitatively it is known as probability. In other words, probability is a concept of measuring the degree of uncertainty.
• Experiment:- An operation which can produce some well-defined results is known as an experiment.
• Random Experiment:- An operation in which an possible results are known but the exact result cannot be predicted in advance in known as random experiment.

Example:-   Throwing of an unbiased die.

                  Tossing of a fair coin.

                  Drawing a card from a well - shuffled pack of cards.

                  When an unbiased coin is tossed, then either a Head (H) or a (T) appears.

• A dice is well balanced cube with its six faces marked with numbers 1, 2, 3, 4, 5, 6 respectively. Hence when we throw a die, the outcome is the number that appears on its upper face.
• Sample Space:- The set of all possible results in a random experiment is called a sample space and it is generally denoted by S.

Example:-   In tossing a coin

                  S = {H, T}

                  In tossing two coins, S = {HH, TT, HT, TH}

                  In throwing a die, S = {1, 2, 3, 4, 5, 6}

• Event:- Any subset of a sample space is called an event.

Example:- In a single throw of a die, the event of getting an prime number is given by E = {2, 3, 5}

Obviously, here sample Space (S) = {1, 2, 3, 4, 5, 6}

Here  i.e., E is a subset of S.

Probability of occurrence of an event

RESULTS ON PROBABILITY

• Probability of a same event is 1.
• Probability of an impossible event = 0. i.e., P(E) = 0
• Sum of the possibilities of an outcome of an experiment is 1. i.e., P (S) = 1

So the possibility of any events lies between 0 and 1. i.e., 

There are 4 honours of each suit viz. Aces, Kings, Queens and Jacks.

• There are three face cards of each suit, king, Queen and Jack.