This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Probability & Experimental Approach”.

1. Two coins were tossed 200 times and the following results were obtained.

Two heads: 55 One head and one tail: 105 Two tails: 40

What is the probability of event of obtaining minimum one head?

a) 0.5

b) 0.8

c) 0.55

d) 0.16

View Answer

Explanation: Number of events of obtaining minimum one head = 55 + 105

= 160

Hence, P (E) = probability of event of obtaining minimum on head

= \(\frac{Number \,of \,events \,of \,obtaining \,minimum \,one \,head}{Number \,of \,total \,trials}\)

= \(\frac{160}{200}\)

= 0.8.

2. A dice was thrown 500 times. Frequencies for the outcomes 1, 2, 3, 4, 5, and 6 are given in the table.

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

Frequency | 78 | 80 | 93 | 79 | 91 | 79 |

What is the probability of getting ‘4’ as outcome?

a) 0.16

b) 0.158

c) 0.156

d) 0.131

View Answer

Explanation: We can see from the table that we get ‘4’ 79 times out of 500 trials.

Therefore, probability of getting ‘4’ as outcome = \(\frac{Event \,of \,occurence \,of \,getting \,’4′}{Total \,number \,of \,trials}\)

= \(\frac{79}{500}\)

= 0.158.

3. Marks obtained by a student in a test is shown in the table below.

Test no. | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Marks | 81 | 87 | 76 | 70 | 90 |

What is the probability that the student has scored more than 80?

a) 0.6

b) 0.8

c) 0.4

d) 0.5

View Answer

Explanation: It can be seen that the student have scored 3 out of 5 times more than 80 marks.

Therefore, probability that the student has scored more than 80 = \(\frac{number \,of \,occurrence \,of \,event}{Total \,number \,of \,trials}\)

= \(\frac{3}{5}\)

= 0.6.

4. 1000 families with 2 children were studied and the following data was collected.

Number of boys in the family | 0 | 1 | 2 |
---|---|---|---|

Number of families | 270 | 415 | 315 |

What is the probability that the family has at least one boy?

a) 0.415

b) 0.270

c) 0.73

d) 0.315

View Answer

Explanation: In this case, having at least one boy means one boy or two boys.

Hence, number of families having at least one boy = 415 + 315 = 730

Therefore, the probability that the family has at least one boy = \(\frac{number \,of \,families \,having \,at \,least \,one \,boy }{Total \,number \,of \,families} = \frac{730}{1000}\)

= 0.73.

5. 1500 drivers were selected for a study to find a relationship between age and accidents. The data is shown in the table below.

Age of drivers(in years) | Number of accidents | ||
---|---|---|---|

0 | 1 | More than 1 | |

18-35 | 285 | 325 | 90 |

35-50 | 145 | 277 | 78 |

Above 50 | 123 | 118 | 59 |

What is the probability of being 18-35 years of age and having more than 1 accidents?

a) 0.06

b) 0.6

c) 0.08

d) 0.1

View Answer

Explanation: We can see that total number of events of being 18-35 years of age and having more than 1 accidents = 90

Total number of events = 1500

Hence, probability of being 18-35 years of age and having more than 1 accidents = \(\frac{90}{1500}\)

= 0.06.

6. 1500 drivers were selected for a study to find a relationship between age and accidents. The data is shown in the table below.

Age of drivers(in years) | Number of accidents | ||
---|---|---|---|

0 | 1 | More than 1 | |

18-35 | 285 | 325 | 90 |

35-50 | 145 | 277 | 78 |

Above 50 | 123 | 118 | 59 |

What is the probability of being elder than 35 years of age and having at least one accident?

a) 0.41

b) 0.25

c) 0.354

d) 0.333

View Answer

Explanation: We can see that total number of events of being elder than 35 years of age and having at least 1 accident = 277 + 78 + 118 + 59

= 532

Total number of events = 1500

Hence, probability of being 18-29 years of age and having more than 1 accidents = \(\frac{532}{1500}\)

= 0.354.

7. 1500 drivers were selected for a study to find a relationship between age and accidents. The data is shown in the table below.

Age of drivers(in years) | Number of accidents | ||
---|---|---|---|

0 | 1 | More than 1 | |

18-35 | 285 | 325 | 90 |

35-50 | 145 | 277 | 78 |

Above 50 | 123 | 118 | 59 |

What is the probability of being 35-50 years of age and having more no accidents?

a) 0.29

b) 0.35

c) 0.09

d) 0.08

View Answer

Explanation: We can see that total number of events of being 35-50 years of age and having more than 1 accidents = 145

Total number of events = 1500

Hence, probability of being 18-29 years of age and having more than 1 accidents = \(\frac{145}{1500}\)

= 0.29.

**Sanfoundry Global Education & Learning Series – Mathematics – Class 9**.

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