Question

The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2, 3 or 5 is

• A. 0.26

Answer 1

The correct option is A 0.26
Method - I:
Number of integers in the set which are divisible by 2 or 3 or 5 =
$n(2\cup 3\cup 5)=n\left(2\right)+n\left(3\right)+n\left(5\right)-n(2\cap 3)-n(3\cap 5)-n(5\cap 2)+n(2\cap 3\cap 5)$
$=50+33+20-16-10-6+3=74$
$\therefore$ The number of integers between 1 and 100 which are not divisible by 2 or 3 or 5
$=n(\overline{2}\cap \overline{3}\cap \overline{5}).$
$=100-n(2\cup 3\cup 5)$
$=100-74=26$

$\therefore \text{Required probability}=\frac{26}{100}=0.26$