Question

Find the probability that a number from 1 to 300 is divisible by 3 or 7 ?

Answer 1

total numbers:  300
divisible by 3:  100
divisible by  7:  42     as  42*7 = 294
divisible by 21:  14     as  21*14 = 294

divisible by 3 or 7:  100+42 -14 = 128

probability = 128/300 = 32/75

Answer 2

Answer:

The probability of a number from 1 to 300 which is being divisible by 3 or 7 is 32/75

Solution:

From 1-300,

Number of numbers (N) = 300

Let the event of getting a number less than 300 that is divisible by 3 be A

Number of numbers divisible by 3  

i.e. n(A) = 100  

[Since, 3 x 100 = 300]

Let the event of getting a number less than 300 that is divisible by 7 be B

Number of numbers divisible by 7  

i.e. n(B) = 42  

[Since, 7 x 42 = 294 which is the nearest number to 300 that is divisible by 7]  

Let the event of getting a number less than 300 that is divisible by 21 be C

Number of numbers divisible by 21  

i.e. n(C) = 14  

[Since, 21 x 14 = 294 which is the nearest number to 300 that is divisible by 21]

Let the event of getting a number from 1 to 300 is divisible by 3 or 7 be E.

Thus, the probability that a number from 1 to 300 is divisible by 3 or 7 is

= P(E)  

$\begin{aligned} = & \frac { n ( A ) + n ( B ) - n ( C ) } { N } \\\\ = & \frac { 100 + 42 - 14 } { 300 } \\\\ = & \frac { 128 } { 300 } \\\\ = & \frac { 32 } { 75 } \end{aligned}$

Therefore, the probability of a number from 1 to 300 which is being divisible by 3 or 7 is 32/75