Question

Probability that a number from 1 to 300 is divisible by either 3 or 7

Answer 1

According to the question they asked to find the probability of the numbers divisible by either 3 or 7 between 1 to 300.

So to find out the numbers divisible by either 3 or 7, we need to find out the LCM of the two numbers that is 21.

Here, we can easily find out the numbers by Arithmetic - Progression.

The first number divisible by either 3 or 7 is 21.

Last number either divisible by 3 or 7 is 294.

To find out number of terms between them, we can use the formula

$\bf{a_{n} = a_{1} + (n - 1)d}$

Where,

$a_{n} = 294 \\ a_{1} = 21 \\ d = 21 \\ n = ?$

294 = 21 + (n-1)(21)

(n-1)(21) = 273

(n-1) = 13

$\bf{Terms\: divisible\:by\:3and7\:=\:14}$

Probability = $\frac{14}{300}$

=$\bf\frac{7}{150}$