JEE Advanced 2021 Paper 2Question 1
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 ___ .
Probability
Answer$214$
Solution
Multiples of 3: 666; of 7: 285; of 21: 95. Count $=666+285-95=856$, $p=\frac{856}{2000}$, $500p=214$.