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Probability in Divisibility | AMC-10A, 2003 | Problem 15

Try this beautiful problem from Probability based on divisibility.

Probability in Divisibility - AMC-10A, 2003- Problem 15


What is the probability that an integer in the set \({1,2,3,…,100}\) is divisible by \(2\) and not divisible by \(3\)?

  • \(\frac {33}{100}\)
  • \(\frac{1}{6}\)
  • \(\frac{17}{50}\)
  • \(\frac{1}{2}\)
  • \(\frac{18}{25}\)

Key Concepts


Number system

Probability

divisibility

Check the Answer


Answer: \(\frac{17}{50}\)

AMC-10A (2003) Problem 15

Pre College Mathematics

Try with Hints


There are total number of integers are \(100\).and numer of integers divisible by \(2\) is \(\frac{100}{2}\)=\(50\). Now we have to find out divisible by \(2\) and not divisible by \(3\). so at first we have to find out the find out the numbers of integers which are divisible by \(2\) and \(3\) both.......

can you finish the problem........

To be divisible by both \(2\) and \(3\), a number must be divisible by the lcm of \((2,3)=6\).

Therefore numbers of integers which are divisible by \(6\)=\(\frac{100}{6}=16\) (between \(1\) & \( 100\))

can you finish the problem........

Therefore the number of integers wcich are divisible by \(2\) and not divisible by \(3\)= \(50 - 16=34\).

So require probability= \(\frac{34}{100}=\frac{17}{50}\)

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