Mathematics · Probability

JEE Advanced 2021 — Paper 2 — Question 23

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 500 p is $\qquad$

Answer: 214

Numerical answer — enter this value.

Step-by-step solution

Total numbers = $2000$ . Number of multiples of 3 = $\left\lfloor \frac{2000}{3} \right\rfloor = 666$ . Number of multiples of 7 = $\left\lfloor \frac{2000}{7} \right\rfloor = 285$ . Number of multiples of 21 (LCM of 3 and 7) = $\left\lfloor \frac{2000}{21} \right\rfloor = 95$ . By inclusion-exclusion, favourable outcomes = $666 + 285 - 95 = 856$ . Probability $p = \frac{856}{2000} = 0.428$ . Required value $500p = 500 \times \frac{856}{2000} = \frac{856}{4} = 214$ .

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2021
Paper: Paper 2
Subject: Mathematics
Chapter: Probability
Topic: Introduction to Probability