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Probability Level 3

Out of the first 100 positive integers, what is the probability that ( x − 20 ) ( x − 40 ) ( x − 30 ) < 0 ? \frac { \left( x-20 \right) \left( x-40 \right) }{ \left( x-30 \right) } <0 ?


The answer is 0.28.

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Utkarsh Bansal by Utkarsh Bansal , 23, India

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4 solutions

By studying the function you realize that for the intervals 0<x<20 and 30<x<40 the fraction has a negative value so you get 19+9 favorable cases out of 100.

7 Helpful 0 Interesting 0 Brilliant 0 Confused

Fantastic approach Mariano sir ,upvoted

Utkarsh Bansal - 6 years, 3 months ago
Saransh Gupya
Mar 9, 2015

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice solution @ @saransh gupya ,upvoted

Utkarsh Bansal - 6 years, 3 months ago

Isn't zero a natural number?!

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Some conventions say it is, some conventions say it isn't. Basically depends on when the book was written and in what country. Either way the answer still comes out as 7 25 \frac{7}{25} since there are 28 28 solutions and 100 100 possibilities.

Caleb Townsend - 6 years, 2 months ago

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There are 29 solutions if 0 is considered a natural number. I agree that both definitions of natural numbers are in common usage.

Andrew Caldwell - 6 years, 2 months ago

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Thanks. Those who answered 0.29 have been marked correct. I've cleaned up the phrasing of the problem accordingly.

In future, if you spot any errors with a problem, you can “report” it by selecting "report problem" in the “dot dot dot” menu in the lower right corner. This will notify the problem creator who can fix the issues.

Calvin Lin Staff - 6 years, 2 months ago

@Gabriel No its not natural numbers start from 1

Utkarsh Bansal - 6 years, 2 months ago

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The definition of natural numbers depends on where you're from, which is why I avoid using it. I've rephrased your question to state "positive integers" instead.

Calvin Lin Staff - 6 years, 2 months ago

zero may or may not be considered a natural number

Vincent Miller Moral - 6 years, 2 months ago
Prateek Sharma
Apr 21, 2015

Whatever be the definition of natural numbers but the question requires positive integers. So 0 can't be included.

0 could have been included if the question has asked first 100 non-negative integers. There is a difference between positive and non-negative. Positive does not include 0 but non-negative does. To know more about this, read http://www.ask.com/math/difference-between-positive-integers-nonnegative-integers-2c9feb6326833062

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