Class 9 Maths Chapter 15 – Probability | NCERT Maths Solutions
Chapter 15 – Probability – In our day to day life, we come across various statements like-
It will probably rain today.
I doubt he will pass the test.
There are 5-50 chances India will win the toss.
The terms like probably, chances, doubt etc. used in the statements refers to the element of uncertainty. These uncertainties can be measured numerically by means of “probability” in many cases.
Coin- coins have two faces head or tail.
Dice- A dice is solid in a form of a cube having 6 faces.
Cards- pack of playing cards with 26 red and 26 black cards. In total 52 cards are there.
Basic concepts of PROBABILITY
The process which produces well defined possible outcomes.
- Random Experiment
An experiment which when performed produces one of the several possible outcomes is called a Random Experiment.
Example- a random experiment can be a tossing of a coin as it is not sure whether it is going to be a head or tail.
Check out another topic of 9th Class Maths Triangles & Types of angle
- The trial of the experiment
Performing the experiment is called the trial of the experiment. Example, if a coin is tossed 20 times, and then each toss is a trial.
- Elementary event
It refers to the outcome of the trial. Example-when two coins are tossed simultaneously, the possible outcomes are HH, HT, TH, and TT. Anyone outcome like TT is called an elementary event of the sample space (HH, TT, HT, TH)
- Compound event
It refers to the collection of 2 or more possible outcomes from an elementary event. Example- random event of tossing two tosses simultaneously and if we define the event for getting exactly one head then HT and RH are two elementary events associated with it, such event is called compound event,
- Trial event
It refers to an event if any one of the elementary event satisfying its condition is an outcome.
In the trial of random experiments, if an event A happens in times, the probability of happening of A is given by P(A)=mn
A coin is tossed 1000 times with the following frequencies
Head-455, Tail 545
then compute the probability of each event.
No. of heads=455, total no of trials 1000, no. of tails =545
Let E be the event of getting head,
P(E)= no. of head/ total no of trial=455/100=0.455
E1 = event of getting tail
P(E1)= )= no. of tail/ total no. of trial=545/100=0.54
The probability of occurrence of head and tail are 0.455 and 0.545
- For any event A associated with an experiment, we have 0≤P(A)≤1
Example- as shown in the above example the value of P€ is between 0 and 1 (0≤P(E)≤1)
- If E1, E2 …En are n elementary events associated with a random experiment then P(E1)+P(E2)+….+P(En)=1
Learn CBSE Class 9 Maths another topic What is Circle? Proves
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