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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