Q. A number $n$ is chosen at random from {1, 2, 3, 4, ……….,1000}. The probability that $n$ is a number that leaves remainder 1 when divided by 7, is
A) $\frac{71}{500}$
B) $\frac{143}{1000}$
C) $\frac{72}{500}$
D) $\frac{71}{1000}$
Explanation
(b)
Let $A$ be the set of all numbers from {1,2,3,…,1000} that leave remainder 1 when divided by 7
$A = \{ 1,8,15,22,\ldots.,995\}$
$\Rightarrow \ n(A) = \frac{995 - 1}{7} + 1 = 143$
$\therefore\ P(A) = \frac{143}{1000}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.