Question

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_____

Answer 1

E = a number which is multiple of 3 or multiple of 7

n(E) = (3, 6, 9, …….., 1998) + (7, 14, 21, ……….., 1995) – (21, 42, 63, ……… 1995)

n(E) = 666+ 285 – 95

n(E) = 856

n(E) = 2000

P(E) = $\frac{856}{2000}$

P(E) × 500 = $\frac{856}{4}$ = 214