Is this TRUE or FALSE...PROBABILITY DEFINITION...?

The sum of the probabilities of all the events in the sample space must equal 1.





I think this is true... am i correct?








2) The mean, variance, and standard deviation should be rounded to one more decimal place than the outcome, X.





I dont know this one... is it true or false?








thanks plz explain!Is this TRUE or FALSE...PROBABILITY DEFINITION...?
The first statement is true: the sum of probabilities is indeed 1.


Explanation: if you express the probabilities as percentages, rather than decimals, you would naturally expect the total to be 100%, wouldn't you?





2) This is about expressing the values with an appropriate level of accuracy for the data. One additional decimal place is a reasonable rule of thumb for most examples.





You also need to consider how many decimal places to give in your result X itself - and this will depend on the quantity and spread of the sample data: if you have just 7 data points, it would be wrong to express the result to 3 decimal places, even if that is what shows on the calculator screen. However, if you had 700 data points, this might be perfectly reasonable.





The magnitude of the values also comes into play: if your 7 values were all between 0.220 and 0.230, you would need to use 3 dp just to express the result, whereas if the values were spread between 1000 and 2000, then your result should probably be rounded to the nearest 10, and have no decimals.





At the end of the day, you need to have a feeling as to whether the number of significant digits expressed in your result is justified by the situation of the problem.Is this TRUE or FALSE...PROBABILITY DEFINITION...?
First one is TRUE.





But it is not the best wording of the question.


The sum of probabilities for possible outcomes of the even must be 1.





2nd one seems true





But it seems like some statistician or engineering rule.


But it makes scenes because if your round down more on input the outcome is rounded down even more. SO you can not have same accuracy e for input as output.
The sum of the probabilities of all the events in the sample space must equal 1. - this is true, definitely true





-The mean, variance, and standard deviation should be rounded to one more decimal place than the outcome, X





now this is problematic as it says-should. I would say FALSE. I had probability and statistic at uni and we rounded everything to 3 decimal places.
Yes, it's true.





Example:





Let's say you have a bag of 7 candies , yum!





2 are blue, 4 are green, and 1 is red.





The odds of picking one at random are: 2 out of 7 for blue, 4 out of seven for green, and 1 out of 7 for red.





these can turned into fractions: 2/7, 4/7, %26amp; 1/7. When you add them together, you get 7/7, which is the same thing as 1.





For the second question, that is also true.
In standard probability the sum of all probabilities must equal 1 and each probability must be non-negative.





The second one is more a rule of thumb than a definition.
what?