JEE Advanced 2021 · Paper 2 · Mathematics Q17

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MathematicsInteger+4Question 55 of 57

A number is chosen at random from the set $\{1, 2, 3, \ldots, 2000\}$ . Let $p$ be the probability that the chosen number is a multiple of 3 or a multiple of 7. Then the value of $500p$ is ____.

Your answer

Answer and worked solution

Official answer: 214

Counting multiples. In $\{1,\dots,2000\}$ :

multiples of 3: 666;
multiples of 7: 285;
multiples of 21: 95.

Inclusion-exclusion. $666+285-95=856$ , so $p=\frac{856}{2000}$ .

Value. $500p=214$ .

Topics:Classical probability Sets and operations

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JEE Advanced 2021 · Paper 2, Mathematics question 17