Advertisements
Advertisements
प्रश्न
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 SO2 | 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. 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.
उत्तर
The total number of trials is 30.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by P (A) and is given by
`P (A) = m/n`
Let A1 be the event that the concentration of sulphur dioxide in a day is 0.12-0.16 parts per million.
The number of times A1 happens is 2.
Therefore, we have
` P(A_1) = 2/30`
`=1/15`
APPEARS IN
संबंधित प्रश्न
A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows: 0 − 20, 20 − 30… 60 − 70, 70 − 100. Then she formed the following table:-
Marks | Number of students |
0 - 20 | 7 |
20 - 30 | 10 |
30 - 40 | 10 |
40 - 50 | 20 |
50 - 60 | 20 |
60 - 70 | 15 |
70 - above | 8 |
Total 90 |
(i) Find the probability that a student obtained less than 20 % in the mathematics test.
(ii) Find the probability that a student obtained marks 60 or above.
To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table.
Opinion | Number of students |
like | 135 |
dislike | 65 |
Find the probability that a student chosen at random
(i) likes statistics, (ii) does not like it
Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes:
Two heads: 95 times
One tail: 290 times
No head: 115 times
Find the probability of occurrence of each of these events.
1500 families with 2 children were selected randomly and the following data were recorded:
Number of girls in a family | 0 | 1 | 2 |
Number of families | 211 | 814 | 475 |
(i) No girl
(ii) 1 girl
(iii) 2 girls
(iv) at most one girl
(v) more girls than boys
In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays.
(i) he hits boundary
(ii) he does not hit a boundary.
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%?
In a survey of 364 children aged 19 – 36 months, it was found that 91 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is ______.
80 bulbs are selected at random from a lot and their life time (in hrs) is recorded in the form of a frequency table given below :
Life time (in hours) | 300 | 500 | 700 | 900 | 1100 |
Frequency | 10 | 12 | 23 | 25 | 10 |
The probability that bulbs selected randomly from the lot has life less than 900 hours is:
A company selected 4000 households at random and surveyed them to find out a relationship between income level and the number of television sets in a home. The information so obtained is listed in the following table:
Monthly income (in Rs) |
Number of Television/household | |||
0 | 1 | 2 | Above 2 | |
< 10000 | 20 | 80 | 10 | 0 |
10000 – 14999 | 10 | 240 | 60 | 0 |
15000 – 19999 | 0 | 380 | 120 | 30 |
20000 – 24999 | 0 | 520 | 370 | 80 |
25000 and above | 0 | 1100 | 760 | 220 |
Find the probability of a household not having any television.
Over the past 200 working days, the number of defective parts produced by a machine is given in the following table:
Number of defective parts |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
Days | 50 | 32 | 22 | 18 | 12 | 12 | 10 | 10 | 10 | 8 | 6 | 6 | 2 | 2 |
Determine the probability that tomorrow’s output will have more than 13 defective parts