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Exercises in Chapter 19 probability Grade 9

Questions in Probability Exercise 19

A die is thrown 300 times and the outcomes are noted as given below:

Outcome | Frequency |
---|---|

1 | 60 |

2 | 72 |

3 | 54 |

4 | 42 |

5 | 39 |

6 | 33 |

When a die is thrown at random, what is the probability of getting a

(i) 3?

(ii) 6?

(iii) 5?

(iv) 1?

The percentages of marks obtained by a student in six-unit tests are given below:

Unit test | Percentage of marks obtained |
---|---|

I | 53 |

II | 72 |

III | 28 |

IV | 46 |

V | 67 |

VI | 59 |

A unit test is selected at random. What is the probability that the student gets more than 60% marks in the test?

On a particular day, at a crossing in a city, the various types of 24 vehicles going past during a time interval were observed under:

Types of vehicle | Frequency |
---|---|

Two-wheelers | 84 |

Three-wheelers | 68 |

Four-wheelers | 88 |

Out of these vehicles, one is chosen at random. What is the probability that the chosen vehicle is a two-wheeler?

On one page of a telephone directory, there are 200 phone numbers. The frequency distribution of their unit’s digits is given below:

Unit's digit | Frequency |
---|---|

0 | 19 |

1 | 22 |

2 | 23 |

3 | 19 |

4 | 21 |

5 | 24 |

6 | 23 |

7 | 18 |

8 | 16 |

9 | 15 |

One of the numbers is chosen at random from the page. What is the probability that the unit’s digit of the

chosen number is (i) 5? (ii) 8?

The following table shows the blood groups of 40 students in a class.

Blood group | Number of students |
---|---|

A | 11 |

B | 9 |

O | 14 |

AB | 6 |

One student of the class is chosen at random. What is the probability that the chosen student has blood group (i) O? (ii) AB?

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

Monthly income (in ₹) | Number of vehicles per family | - | - | - |
---|---|---|---|---|

- | 0 | 1 | 2 | 3 or more |

Less than ₹ 25000 | 10 | 160 | 25 | 0 |

₹ 25000 - ₹ 30000 | 0 | 305 | 27 | 2 |

₹ 30000 - ₹ 35000 | 1 | 535 | 29 | 1 |

₹ 35000 - ₹ 40000 | 2 | 469 | 59 | 25 |

₹ 40000 or more | 1 | 579 | 82 | 88 |

Suppose a family is chosen at random. Find the probability that the family chosen is

(i) earning ₹ 25000 - ₹ 30000 per month and owing exactly 2 vehicles.

(ii) earning ₹ 40000 or more per month and owing exactly 1 vehicle.

(iii) earning less than ₹ 25000 per month and not owing any vehicle.

(iv) earning ₹ 35000 - ₹ 40000 per month and owing 2 or more vehicles.

(v) owing not more than 1 vehicle.

The table given below shows the ages of 75 teachers in a school.

Age (in years) | Number of teachers |
---|---|

18 - 29 | 3 |

30 - 39 | 27 |

40 - 49 | 37 |

50 - 59 | 8 |

A teacher from this school is chosen at random. What is the probability that the selected teacher is

(i) 40 or more than 40 years old?

(ii) of any age lying between 30-39 years (including both)?

(iii) 18 years or more and 49 years or less?

(iv) 18 years or more old?

(v) above 60 years of age?

Following are the ages (in years) of 360 patients, getting medical treatment in a hospital:

Age (in years) | Number of patients |
---|---|

10-20 | 90 |

20-30 | 50 |

30-40 | 60 |

40-50 | 80 |

50-60 | 50 |

60-70 | 30 |

On of the patients is selected at random.

What is the probability that his age is

(i) 30 years or more but less than 40 years?

(ii) 50 years or more but less than 70 years?

(iii) 10 years or more but less than 40 years?

(iv) 10 years or more?

(v) less than 10 years?

The marks obtained by 90 students of a school in mathematics out of 100 are given as under:

Marks | Number of patients |
---|---|

0-20 | 7 |

20-30 | 8 |

30-40 | 12 |

40-50 | 25 |

50-60 | 19 |

60-70 | 10 |

70 and above | 9 |

From these students, a student is chosen at random.

What is the probability that the chosen student

(i) gets 20% or fewer marks?

(ii) gets 60% or more marks?

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