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3

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

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

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.

4

1500 families with 2 children were delected randomly and the following data were recorded:

No. of girls in a family : | 0 | 1 | 2 |

No. of families : | 211 | 814 | 475 |

If a family is chosen at random, compute the probability that it has:

(i) No girl

(ii) 1 girl

(iii) 2 girls

(iv) At most one girl

(v) More girls than boys.

6

The percentage of marks obtained by a student in monthly unit tests are given below :

Unit test : | I | II | III | IV | V |

% of marks obtained: | 69 | 71 | 73 | 68 | 76 |

Find the probability that the student gets :

(i)More than 70% marks

(ii) Less than 70% marks

(iii) A distinction.

7

To know the opinion of the students about Mathematics, a survey of 200 students was conducted. The data is recorded in the following tables:

Opinion: | Like | Dislike |

No. of students : | 135 | 65 |

Find the probability that a student chosen at random

(i) likes Mathematics

(ii) does not like it.

9

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.

10

Following table shows the birth month of 40 students of class IX.

Jan. |
Feb. |
March |
April |
May |
June |
July |
Aug. |
Sep. |
Oct. |
Nov. |
Dec. |

3 |
4 |
2 |
2 |
5 |
1 |
2 |
6 |
3 |
4 |
4 |
4 |

Find the probability that a student was born in August.

11

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 | 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. of 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.

12

A company selected 2400 families at random and survey them to determine a relationship between income level and the number of vehicles in a home. The information gathered is listed in the table below :

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

0 | 1 | 2 | Above 2 | |

Less than 7000 7000-10000 10000-13000 13000-16000 16000 or more | 10 0 1 2 1 | 160 305 535 469 579 | 25 27 29 29 82 | 0 2 1 25 88 |

If a family is chosen find the probability that the family is:

(i) earning Rs. 10,000 – 13,000 per month and owning exactly 2 vehicles.

(ii) earning Rs. 16,000 or more per month and owning exactly 1 vehicles.

(iii) earning less than Rs. 7,000 per month and does not own any vehicles.

(iv) earning Rs. 13,000 – 16,000 per month and owning more than 2 vehicles.

(v) owning not more than 1 vehicle.

(vi)owning at least one vehicle.

13

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

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

No. of lamps | 14 | 56 | 60 | 86 | 74 | 62 | 48 |

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

(i) less than 400

(ii) between 300 to 800 hours

(iii)at least 700 hours.

14

Given below is the frequency distribution of wages (in Rs.) of 30 workers in a certain factory :

Wages (in Rs.) | 110-130 | 130-150 | 150-170 | 170-190 | 190-210 | 210-230 | 230-250 |

No. of workers | 3 | 4 | 5 | 6 | 5 | 4 | 3 |

A worker is selected atr random. Find the probability that his wages are :

(i) less than Rs. 150

(ii) at least Rs. 210

(iii) more than or equal to 150 but less than Rs. 210.

7

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

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

Frequency | 23 | 72 | 77 | 28 |

Find the probability of getting at most two heads.

7

A dice is rolled 600 times and the occurrence of the outcomes 1, 2, 3, 4, 5 and 6 are given below :

Outcome | 1 | 2 | 3 | 4 | 5 | 6 |

Frequency | 200 | 30 | 120 | 100 | 50 | 100 |

The probability of getting a prime number is

8

The percentage of attendance of different classes in a year in a school is given below :

Class: | X | IX | VIII | VII | VI | V |

Attendance: | 30 | 62 | 85 | 92 | 76 | 55 |

What is the probability that the class attendance is more than 75%?