Skip to main content

An integer from 100 through 999, inclusive, is to be chosen at random. What is the probability that the number chosen will have 0 as at least 1 digit?

Hello!


Probability is (the quantity of numbers having zero) / (the total quantity of numbers).


It is obvious that the total quantity of numbers is  `(999 - 100 + 1) = 900.`  The quantity of numbers among these having at least one zero have to be computed.


Zero may be at the ones position or tens position, not hundreds. It is obvious that one-tenth of these `900` numbers has zero at ones position, this is `90` numbers. Also `90` numbers have zero at the tens position.


But the total quantity of numbers with zeros is NOT 90+90, because some numbers have zeros at both ones and tens. There are 9 such numbers (100, 200, 300, ... , 900).


So there are `90+90-9=9*19` numbers with zeros, and the probability is


`(9*19)/900=19/100=0.19` or 19%. This is the answer.

Comments

Post a Comment

Popular posts from this blog

etymology - Origin of the greeting "Sweet dreams".

Does anybody know the etymology of the phrase "sweet dreams"? I tried googling but did not find anything satisfying. Is this a relatively new phrase of the modern world or has this been in use for some time? I think it's the latter one. Answer The OED has the interjection as "a farewell to someone going to bed" from the 20th century: 1908 Sears Roebuck Catal. 198/1 Tenor Solos..Good Bye, Sweet Dreams, Good Bye. But it goes back until at least the 19th and possibly 18th centuries. John Wolcot, writing under the pseudonym of Peter Pindar, used it in his poem "Orson and Ellen; A Legendary Tale" published in 1801: Also from 1801 in The infernal Quixote (Page 287) by Charles Lucas: In the March 1776 of The Universal Magazine was published "The Serenade. A Pastoral Tale. From the German of Gesner" , where the shepherd Daphnis watches over his beloved as she sleeps and sings: The same tale appears in 1776's as Idyl XI, " Daphnis ...
Post a Comment
Read more

Is there a word/phrase for "unperformant"?

As a software engineer, I need to sometimes describe a piece of code as something that lacks performance or was not written with performance in mind. Example: This kind of coding style leads to unmaintainable and unperformant code. Based on my Google searches, this isn't a real word. What is the correct way to describe this? EDIT My usage of "performance" here is in regard to speed and efficiency. For example, the better the performance of code the faster the application runs. My question and example target the negative definition, which is in reference to preventing inefficient coding practices. Answer This kind of coding style leads to unmaintainable and unperformant code. In my opinion, reads more easily as: This coding style leads to unmaintainable and poorly performing code. The key to well-written documentation and reports lies in ease of understanding. Adding poorly understood words such as performant decreases that ease. In addressing the use of such a poorly ...
Post a Comment
Read more

What are the similarities between the relationships of the characters in The Outsiders and Romeo and Juliet?

At first glance, it might appear as if the characters in  The Outsiders  by S. E. Hinton and  Romeo and Juliet  by William Shakespeare do not have much in common; however, when one isolates the core of the conflicts, it becomes clear that the relationships in both stories are rooted in rivalry and secrecy.  In both  The Outsiders  and  Romeo and Juliet , an overarching theme is rivalry. While   socioeconomic status separates the greasers from the Socs in The Outsiders , last names separates the Montagues from the Capulets, who appear to be relatively equal in terms of socioeconomic status. Due to these rivalries, there are instances of deadly interactions in both stories. In  The Outsiders , Johnny kills Bob (whether his actions were justified or not is debatable). In  Romeo and Juliet , Romeo kills Tybalt and Paris, and Tybalt kills Mercutio. These deaths have profound effects on the main characters. In Ponyboy's case, the Johnny's death and other events in the novel inspire h...
Post a Comment
Read more