$A$ die is thrown $1000$ times with the frequencies for the outcomes $1, 2, 3, 4, 5$ and $6$ as given in the following table:
Outcome $1$ $2$ $3$ $4$ $5$ $6$ Frequency $179$ $150$ $157$ $149$ $175$ $190$
Find the probability of getting each outcome.
| Outcome | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ |
| Frequency | $179$ | $150$ | $157$ | $149$ | $175$ | $190$ |
Find the probability of getting each outcome.
(N/A) Let $E_i$ denote the event of getting the outcome $i$,where $i = 1, 2, 3, 4, 5, 6$.
The probability of an event is given by the formula: $P(E) = \frac{\text{Number of trials in which the event happened}}{\text{Total number of trials}}$.
Here,the total number of trials is $1000$.
$P(E_1) = \frac{179}{1000} = 0.179$
$P(E_2) = \frac{150}{1000} = 0.150$
$P(E_3) = \frac{157}{1000} = 0.157$
$P(E_4) = \frac{149}{1000} = 0.149$
$P(E_5) = \frac{175}{1000} = 0.175$
$P(E_6) = \frac{190}{1000} = 0.190$
Note that the sum of all probabilities is $0.179 + 0.150 + 0.157 + 0.149 + 0.175 + 0.190 = 1$.
The probability of an event is given by the formula: $P(E) = \frac{\text{Number of trials in which the event happened}}{\text{Total number of trials}}$.
Here,the total number of trials is $1000$.
$P(E_1) = \frac{179}{1000} = 0.179$
$P(E_2) = \frac{150}{1000} = 0.150$
$P(E_3) = \frac{157}{1000} = 0.157$
$P(E_4) = \frac{149}{1000} = 0.149$
$P(E_5) = \frac{175}{1000} = 0.175$
$P(E_6) = \frac{190}{1000} = 0.190$
Note that the sum of all probabilities is $0.179 + 0.150 + 0.157 + 0.149 + 0.175 + 0.190 = 1$.
Explore More
Similar Questions
$A$ tyre manufacturing company kept a record of the distance covered before a tyre needed to be replaced. The table shows the results of $1000$ cases.
Distance (in $km$) less than $4000$ $4000$ to $9000$ $9001$ to $14000$ more than $14000$ Frequency $20$ $210$ $325$ $445$
If you buy a tyre of this company,what is the probability that:
$(i)$ it will need to be replaced before it has covered $4000 \, km$?
$(ii)$ it will last more than $9000 \, km$?
$(iii)$ it will need to be replaced after it has covered somewhere between $4000 \, km$ and $14000 \, km$?
| Distance (in $km$) | less than $4000$ | $4000$ to $9000$ | $9001$ to $14000$ | more than $14000$ |
| Frequency | $20$ | $210$ | $325$ | $445$ |
If you buy a tyre of this company,what is the probability that:
$(i)$ it will need to be replaced before it has covered $4000 \, km$?
$(ii)$ it will last more than $9000 \, km$?
$(iii)$ it will need to be replaced after it has covered somewhere between $4000 \, km$ and $14000 \, km$?
Medium
View SolutionThe following frequency distribution table shows the concentration of sulphur dioxide $(SO_2)$ in the air in parts per million $(ppm)$ of a certain city for $30$ days. Using this table,find the probability of the concentration of sulphur dioxide being in the interval $0.12 - 0.16$ on any of these days.
Concentration of $SO_2$ (in $ppm$) Number of days (frequency) $0.00-0.04$ $4$ $0.04-0.08$ $9$ $0.08-0.12$ $9$ $0.12-0.16$ $2$ $0.16-0.20$ $4$ $0.20-0.24$ $2$ Total $30$
| Concentration of $SO_2$ (in $ppm$) | Number of days (frequency) |
| $0.00-0.04$ | $4$ |
| $0.04-0.08$ | $9$ |
| $0.08-0.12$ | $9$ |
| $0.12-0.16$ | $2$ |
| $0.16-0.20$ | $4$ |
| $0.20-0.24$ | $2$ |
| Total | $30$ |
Medium
View Solution$A$ teacher wanted to analyze 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 $0-20$ $7$ $20-30$ $10$ $30-40$ $10$ $40-50$ $20$ $50-60$ $20$ $60-70$ $15$ $70$ and 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.
| Marks | Number of students |
| $0-20$ | $7$ |
| $20-30$ | $10$ |
| $30-40$ | $10$ |
| $40-50$ | $20$ |
| $50-60$ | $20$ |
| $60-70$ | $15$ |
| $70$ and 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.
Medium
View SolutionThe record of a weather station shows that out of the past $250$ consecutive days,its weather forecasts were correct $175$ times.
$(i)$ What is the probability that on a given day it was correct?
$(ii)$ What is the probability that it was not correct on a given day?
$(i)$ What is the probability that on a given day it was correct?
$(ii)$ What is the probability that it was not correct on a given day?
Medium
View SolutionOn one page of a telephone directory,there were $200$ telephone numbers. The frequency distribution of their unit place digit (for example,in the number $25828573$,the unit place digit is $3$) is given in the table below:
Digit $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ Frequency $22, 26, 22, 22, 20, 10, 14, 28, 16, 20$
Without looking at the page,a number is chosen at random. What is the probability that the digit in its unit place is $6$?
| Digit | $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ |
| Frequency | $22, 26, 22, 22, 20, 10, 14, 28, 16, 20$ |
Without looking at the page,a number is chosen at random. What is the probability that the digit in its unit place is $6$?
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo