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Citation from Khan Academy:

Problem sentence:

Hugo plans to buy packs of baseball cards until he gets the card of his favorite player, but he only has enough money to buy at most 4 packs. Suppose that each pack has probability 0.2 of containing the card Hugo is hoping for.

< The probability information in a table comes here >

Question sentence

What is the probability that Hugo buys at most 3 packs of cards?

My question:

Is the above question sentence correct and natural? I think the following sentence, which I rephrased the question sentence to, is more natural to me.

What is the probability that Hugo buys 3 or less packs of cards?

2 Answers 2

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The following is natural sounding to mathematicians.
However, it does not sound natural to anyone besides a mathematician:

What is the probability that Hugo buys at most 3 packs of cards?

The following is wrong:

What is the probability that Hugo buys 3 or less packs of cards?

There are two words in English which have almost the same meaning:

  1. "LESS"
  2. "FEWER"

Consider nouns like "card"

If it is okay English to use a letter "s" at the end of word X, then write "FEWER [X]s"

If it is NOT correct English to use a letter "s" at the end of word X, then write "LESS [X]"

Noun without "s" Noun without "s" Is the "s" okay? "Less" or "fewer"
information informations "s" at the end is WRONG Less Information
patience patiences "s" at the end is WRONG Less Patience
singing singings "s" at the end is WRONG Less Singing
fishing fishings "s" at the end is WRONG Less Fishing
butter butters "s" at the end is WRONG Less Butter
air airs "s" at the end is WRONG
helium heliums "s" at the end is WRONG
petrol petrols "s" at the end is WRONG
concrete concretes "s" at the end is WRONG
gravity gravities "s" at the end is WRONG
thunder thunders "s" at the end is WRONG Less Thunder
car cars "s" at the end is okay 😊 Fewer Cars
card cards "s" at the end is okay 😊 Fewer Cards
house houses "s" at the end is okay 😊 Fewer Houses
computer computers "s" at the end is okay 😄 Fewer Computers

The best way to word your sentence is as one of the following:

  • What is the probability that Hugo buys 3 or fewer packs of cards?
  • What is the probability that Hugo buys 1, 2, or 3 packs of cards, or none at all?
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  • I totally disagree with your statement about mathematicians. Take the sentence "until now, you could book at most four months in advance". collinsdictionary.com/dictionary/english/at-most ......... The sentence "What is the probability that Hugo buys 3 or fewer packs of cards?" is also incorrect and should be What is the probability that Hugo buys fewer than 3 packs of cards? and "What is the probability that Hugo buys 1, 2, or 3 packs of cards, or none at all?" Is both mathematically different and grammatically incorrect.
    – Brad
    Jun 6, 2021 at 5:23
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What is the probability that Hugo buys at most 3 packs of cards?

sounds good.


What is the probability that Hugo buys 3 or less packs of cards?

This sounds awkward (Order of adjectives). Think about buying a piece of cloth or some vegetables.

You would buy less than a meter or more than a meter of cloth. but not a meter less or a meter more as it would alter the meaning of the sentence.

You could buy just less than a pound of tomatoes or just more than a pound but not a pound less or a pound more.


To use less in this sentence try this

>What is the probability that Hugo buys less than 3 packs of cards?

However this is now mathematically incorrect


>What is the probability that Hugo buys less than 4 packs of cards?

sounds better, but is still mathematically incorrect as he could theoretically buy 3.5 packs. therefore the correct statement would be

>What is the probability that Hugo buys at most three packs of cards?

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