Maharashtra Board Class 10 Maths Part I Chapter 5 Probability PDF Download

Probability

Probability: Introduction

Random experiment and its outcome

Sample space and event

Probability of an event

Let's discuss.

Teacher: Friends, this box contains folded chits. The number of chits is exactly the same as the number of students in our class. Each student should pick one chit. Names of different plants are written on the chits. No two chits bear the same name of the plant. Let us see who gets the chit having the name 'Basil'. Make a line in the order of your roll numbers. No one will unfold the chit until the last student takes his chit.

Aruna: Sir, I am the first one in a line, but I do not want to pick a chit first, as the possibility of getting 'basil' chit from all the chits is very low.

Zarina: Sir, I am the last student in the row, I do not want to pick the chit at last as the chit containing the name 'basil' will most likely be picked up by some one else before my turn.

The first and the last student feel that for each of them, the possibility of getting the chit having the name 'basil' is very low. The above conversation indicates the thinking of less or more possibility.

We use the following words to express the possibility in our daily conversation.

Probable

may be

impossible

sure

nearly

50 - 50

Read the following statements regarding predictions (possibilities for the future).

Most probably the rain will start from today.

The inflation is likely to rise.

It is impossible to defeat Indian cricket team in the next match.

I will surely get first class.

There is no possibility of Polio infection if a child is given the polio vaccine in time.

Teacher's Note

In India, we often hear weather reports saying "rain is probable today." This is probability in real life. When we talk about something happening or not happening, we use probability ideas.

Exam Trick

Remember: Probability is always between 0 and 1. If someone tells you the probability is 1.5 or 2, it is wrong! Just like a student can score between 0 and 100 marks, probability stays between 0 and 1.

Points to Remember

Probability tells us how likely something will happen.

We use words like "probable," "impossible," and "sure" to talk about possibility.

Higher probability means the event is more likely to happen.

Lower probability means the event is less likely to happen.

Let's study.

The adjoining picture shows a 'toss' before a cricket match.

What are the possibilities?

So here there are 2 possibilities.

Activity 1

Let each student in the class toss a coin once. What will you get?

(Teacher writes the observations on the board in a table.)

Activity 2

Ask each student to toss the same coin twice. What are the possibilities?

Activity 3

Now throw a die, once. What are the different possibilities of getting dots on the upper face?

Each of these is a possible result of throwing a die.

Teacher's Note

In India, when children play games, they toss coins or roll dice. This is a random experiment. The child does not know which side will come up, but knows what can come up.

Exam Trick

Remember: When you toss a coin, only two things can happen - Head or Tail. Just like your Aadhaar card has only two sides - chip and paper. One of them must appear!

Points to Remember

A random experiment has results we know beforehand, but cannot predict which one will happen.

Tossing a coin and rolling a die are random experiments.

Tossing a coin gives 2 possible results: Head or Tail.

Rolling a die gives 6 possible results: 1, 2, 3, 4, 5, or 6.

Let's learn.

Random Experiment

The experiment in which all possible results are known in advance but none of them can be predicted with certainty and there is equal possibility for each result is known as a 'Random experiment'.

For example, Tossing a coin, throwing a die, picking a card from a set of cards bearing numbers from 1 to 50, picking a card from a pack of well shuffled playing cards, etc.

Teacher's Note

In your school, when the teacher picks a student's name from the roll book to ask a question, it is a random experiment. No one knows whose name will be picked, but we know all names that can be picked.

Exam Trick

Remember: "Random" means we cannot predict. So if a teacher always picks the last row students, it is not a random experiment. It becomes random only when all students have equal chance.

Points to Remember

All possible results are known before the experiment.

We cannot predict which result will happen.

Each result has an equal chance of happening.

Outcome

Result of a random experiment is known as an 'Outcome'.

Ex. (1) In a random experiment of tossing a coin - there are only two outcomes.

Head (H) or Tail (T)

(2) In a random experiment of throwing a die, there are 6 outcomes, according to the number of dots on the six faces of the die.

1 or 2 or 3 or 4 or 5 or 6.

(3) In a random experiment of picking a card bearing numbers from 1 to 50, there are 50 outcomes.

(4) A card is drawn randomly from a pack of well shuffled playing cards. There are 52 cards in a pack as shown below.

Total cards 52

26 red cards 26 black cards

13 heart cards 13 diamond cards 13 club cards 13 spade cards

In a pack of playing cards there are 4 sets, namely heart, diamond, club and spade. In each set there are 13 cards as King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2 and Ace.

King, Queen and Jack are known as face cards. In each pack of cards there are 4 cards of king, 4 cards of Queen and 4 cards of Jack. Thus total face cards are 12.

Teacher's Note

In India, children play card games during festivals. A pack has 52 cards with 4 different suits. Each suit has 13 cards. This is a standard pack used everywhere in the world.

Exam Trick

Remember: There are 52 cards total. 26 are red (hearts and diamonds) and 26 are black (clubs and spades). There are 4 face cards of each type - 4 Kings, 4 Queens, and 4 Jacks. So total face cards = 4 + 4 + 4 = 12.

Points to Remember

An outcome is one possible result of a random experiment.

A coin toss has 2 outcomes: Head or Tail.

A die roll has 6 outcomes: 1, 2, 3, 4, 5, or 6.

A playing card pack has 52 outcomes.

Equally Likely Outcomes

If a die is thrown, any of the numbers from 1, 2, 3, 4, 5, 6 may appear on the upper face. It means that each number is equally likely to occur. However, if a die is so formed that a particular face come up most often, then that die is biased. In this case the outcomes are not likely to occur equally.

Here, we assume that objects used for random experiments are fair or unbiased. A given number of outcomes are said to be equally likely if none of them occurs in preference to others. For example if a coin is tossed, possibilities of getting head or tail are equal. A die, having numbers from 1 to 6 on its different faces, is thrown. Check the possibility of getting one of the numbers. Here all the outcomes are equally likely.

Teacher's Note

When you toss a coin made of metal, both sides have equal chance to come up. But if the coin is biased or bent, one side may come up more often. For fair games, we must use fair coins and fair dice.

Exam Trick

Remember: "Equally likely" means each outcome has the same chance. Think of it like a fair raffle in your school - every ticket has the same chance to win. If the raffle is rigged, it is not equally likely.

Points to Remember

Equally likely outcomes means each outcome has the same chance of happening.

A fair coin and fair die give equally likely outcomes.

A biased or bent coin does not give equally likely outcomes.

When rolling a fair die, each number 1 to 6 has equal chance.

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