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#### Chapters

1 - Number Systems2 - Polynomials

3 - Coordinate Geometry

4 - Linear Equations in two Variables

5 - Introduction to Euclid's Geometry

6 - Lines and Angles

7 - Triangles

8 - Quadrilaterals

9 - Areas of Parallelograms and Triangles

10 - Circles

11 - Constructions

12 - Heron's Formula

13 - Surface Area and Volumes

14 - Statistics

15 - Probability

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### Chapter 15 - Probability

#### Pages 284 - 285

In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

1500 families with 2 children were selected randomly, and the following data were recorded:-

Number of girls in a family | 2 | 1 | 0 |

Number of families | 475 | 814 | 211 |

Compute the probability of a family, chosen at random, having

(i) 2 girls (ii) 1 girl (iii) No girl

Also check whether the sum of these probabilities is 1.

In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained:-

Find the probability that a student of the class was born in August.

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:-

Outcome | 3 heads | 2 heads | 1 head | No head |

Frequency | 23 | 72 | 77 | 28 |

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:-

Monthly income (in Rs.) |
Vehicles per family | |||

0 | 1 | 2 | Above 2 | |

Less than 7000 | 10 | 160 | 25 | 0 |

7000 – 10000 | 0 | 305 | 27 | 2 |

10000 – 13000 | 1 | 535 | 29 | 1 |

13000 – 16000 | 2 | 469 | 59 | 25 |

16000 or more | 1 | 579 | 82 | 88 |

Suppose a family is chosen, find the probability that the family chosen is

(i) earning Rs 10000 − 13000 per month and owning exactly 2 vehicles.

(ii) earning Rs 16000 or more per month and owning exactly 1 vehicle.

(iii) earning less than Rs 7000 per month and does not own any vehicle.

(iv) earning Rs 13000 − 16000 per month and owning more than 2 vehicles.

(v) owning not more than 1 vehicle.

A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows: 0 − 20, 20 − 30… 60 − 70, 70 − 100. Then she formed the following table:-

Marks | Number of students |

0 - 20 | 7 |

20 - 30 | 10 |

30 - 40 | 10 |

40 - 50 | 20 |

50 - 60 | 20 |

60 - 70 | 15 |

70 - above | 8 |

Total 90 |

(i) Find the probability that a student obtained less than 20 % in the mathematics test.

(ii) Find the probability that a student obtained marks 60 or above.

To know the opinion of the students about the subject *statistics*, a survey of 200 students was conducted. The data is recorded in the following table.

Opinion | Number of students |

like | 135 |

dislike | 65 |

Find the probability that a student chosen at random

(i) likes statistics, (ii) does not like it

The distance (in km) of 40 engineers from their residence to their place of work were found as follows.

5 | 3 | 10 | 20 | 25 | 11 | 13 | 7 | 12 | 31 |

19 | 10 | 12 | 17 | 18 | 11 | 32 | 17 | 16 | 2 |

7 | 9 | 7 | 8 | 3 | 5 | 12 | 15 | 18 | 3 |

12 | 14 | 2 | 9 | 6 | 15 | 15 | 7 | 6 | 12 |

What is the empirical probability that an engineer lives:-

(i) less than 7 km from her place of work?What is the empirical probability that an engineer lives:

(ii) more than or equal to 7 km from her place of work?

(iii) within 1/2 km from her place of work?

Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg):- 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00

Find the probability that any of these bags chosen at random contains more than 5 kg of flour.

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.

Blood Group |
Number of Students |

A | 9 |

B | 6 |

AB | 3 |

O | 12 |

Total | 30 |

The above frequency distribution table represents the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB.

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