#### Topics

##### Number Systems

##### Number Systems

##### Algebra

##### Polynomials

##### Linear Equations in Two Variables

##### Coordinate Geometry

##### Geometry

##### Coordinate Geometry

##### Mensuration

##### Introduction to Euclid’S Geometry

##### Lines and Angles

- Introduction to Lines and Angles
- Basic Terms and Definitions
- Intersecting Lines and Non-intersecting Lines
- Parallel Lines
- Pairs of Angles
- Parallel Lines and a Transversal
- Lines Parallel to the Same Line
- Angle Sum Property of a Triangle

##### Statistics and Probability

##### Triangles

##### Quadrilaterals

- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Angle Sum Property of a Quadrilateral
- Types of Quadrilaterals
- Another Condition for a Quadrilateral to Be a Parallelogram
- Theorem of Midpoints of Two Sides of a Triangle
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram

##### Circles

- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Angle Subtended by a Chord at a Point
- Perpendicular from the Centre to a Chord
- Circles Passing Through One, Two, Three Points
- Equal Chords and Their Distances from the Centre
- Angle Subtended by an Arc of a Circle
- Cyclic Quadrilateral

##### Areas - Heron’S Formula

##### Surface Areas and Volumes

##### Statistics

##### Algebraic Expressions

##### Algebraic Identities

##### Area

##### Constructions

- Introduction of Constructions
- Basic Constructions
- Some Constructions of Triangles

##### Probability

## Notes

The likelihood of something happening is called the probability.**Terms related to probability:****Experiment :** An activity which produces an outcome or result is called an experiment.

**random Experiment :** An Experiment in which exact outcome cannot be predicted in advance.

For example:

1) rolling a dice

2) Drawing a card from well-shuffled pack of playing cards

3) Tossing a coin**Trial :** Performing an experiment is called a trial.**Event :** Each possible outcomes of an experiment is called event.**Probability of an event :** In a random experiment if 'n' is the total number of trials, then the empirical probability of the event E is P(E).

P(E) =

`"Number of trials happened in which event happened" / " Total number of trials"`

i.e. P(E) =`"Number of trials happened in which event happened" / n `

The Probability of an event lies between 0 and 1 (0 and 1 inclusive).

#### Shaalaa.com | Probability Experimental Approach

#### Related QuestionsVIEW ALL [67]

Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes:

Outcome: | No head | One head | Two heads | Three heads |

Frequency: | 14 | 38 | 36 | 12 |

If the three coins are simultaneously tossed again, compute the probability of:

(i) 2 heads coming up.

(ii) 3 heads coming up.

(iii) at least one head coming up.

(iv) getting more heads than tails.

(v) getting more tails than heads.

Given below is the frequency distribution table regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days.

Conc. of SO_{2} |
0.00-0.04 | 0.04-0.08 | 0.08-0.12 | 0.12-0.16 | 0.16-0.20 | 0.20-0.24 |

No. days: | 4 | 8 | 9 | 2 | 4 | 3 |

Find the probability of concentration of sulphur dioxide in the interval 0.12-0.16 on any of these days.

The following table gives the life time of 400 neon lamps:

Life time (in hours) |
300-400 | 400-500 | 500-600 | 600-700 | 700-800 | 800-900 | 900-1000 |

Number of lamps: | 14 | 56 | 60 | 86 | 74 | 62 | 48 |

A bulb is selected of random, Find the probability that the the life time of the selected bulb is:

(i) less than 400

(ii) between 300 to 800 hours

(iii) at least 700 hours.

Concentration of SO_{2} (in ppm) |
Number of days (Frequency) |

0.00 − 0.04 | 4 |

0.04 − 0.08 | 9 |

0.08 − 0.12 | 9 |

0.12 − 0.16 | 2 |

0.16 − 0.20 | 4 |

0.20 − 0.24 | 2 |

Total | 30 |

The above frequency distribution table represents the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12 − 0.16 on any of these days.