# Mathematics Questions and Answers – Probability & Experimental Approach

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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

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 Frequency 1 2 3 4 5 6 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

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. Marks 1 2 3 4 5 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

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 Number of families 0 1 2 270 415 315

What is the probability that the family has at least one boy?
a) 0.415
b) 0.270
c) 0.73
d) 0.315

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

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

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

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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