Advertisements
Advertisements
प्रश्न
Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
| Outcome | 3 heads | 2 heads | 1 head | No head |
| Frequency | 23 | 72 | 77 | 28 |
Find the probability of getting at most two heads.
उत्तर
The total number of trials is 200.
Let A be the event of getting at most two heads.
The number of times A happens is 28 + 77 +72 = 177 .
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`
Therefore, we have P(A) = `177/200`.
APPEARS IN
संबंधित प्रश्न
An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:-
|
Monthly income (in Rs.) |
Vehicles per family | |||
| 0 | 1 | 2 | Above 2 | |
| Less than 7000 | 10 | 160 | 25 | 0 |
| 7000 – 10000 | 0 | 305 | 27 | 2 |
| 10000 – 13000 | 1 | 535 | 29 | 1 |
| 13000 – 16000 | 2 | 469 | 59 | 25 |
| 16000 or more | 1 | 579 | 82 | 88 |
Suppose a family is chosen, find the probability that the family chosen is
(i) earning Rs 10000 − 13000 per month and owning exactly 2 vehicles.
(ii) earning Rs 16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than Rs 7000 per month and does not own any vehicle.
(iv) earning Rs 13000 − 16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle.
| Blood Group | Number of Students |
| A | 9 |
| B | 6 |
| AB | 3 |
| O | 12 |
| Total | 30 |
The above frequency distribution table represents the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB.
The percentage of marks obtained by a student in monthly unit tests are given below:
| Unit test: | I | II | III | IV | V |
| Percentage of marks obtained: | 69 | 71 | 73 | 68 | 76 |
Find the probability that the student gets:
(i) more than 70% marks
(ii) less than 70% marks
(iii) a distinction
Eleven bags of wheat flour, each marked 5 Kg, actually contained the following weights of flour (in kg):
4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00
Find the probability that any of these bags chosen at random contains more than 5 kg of flour.
Given below is the frequency distribution of wages (in Rs) of 30 workers in a certain factory:
| Wages (in Rs) | 110-130 | 130-150 | 150-170 | 170-190 | 190-210 | 210-230 | 230-250 |
| No. of workers | 3 | 4 | 5 | 6 | 5 | 4 | 3 |
A worker is selected at random. Find the probability that his wages are:
(i) less than Rs 150
(ii) at least Rs 210
(iii) more than or equal to 150 but less than Rs 210.
Define a trial.
A big contains 4 white balls and some red balls. If the probability of drawing a white ball from the bag is `2/5`, find the number of red balls in the bag.
In a sample study of 642 people, it was found that 514 people have a high school certificate. If a person is selected at random, the probability that the person has a high school certificate 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 |
One bulb is selected at random from the lot. The probability that its life is 1150 hours, is
A recent survey found that the ages of workers in a factory is distributed as follows:
| Age (in years) | 20 – 29 | 30 – 39 | 40 – 49 | 50 – 59 | 60 and above |
| Number of workers | 38 | 27 | 86 | 46 | 3 |
If a person is selected at random, find the probability that the person is under 60 but over 39 years
