# GATE | GATE-CS-2014-(Set-2) | Question 65

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

(A) 0.259
(B) 0.459
(C) 0.325
(D) 0.225

Explanation:

```There are total 100 numbers, out of which

50 numbers are divisible by 2,
33 numbers are divisible by 3,
20 numbers are divisible by 5

Following are counted twice above
16 numbers are divisible by both 2 and 3
10 numbers are divisible by both 2 and 5
6 numbers are divisible by both 3 and 5

Following is counted thrice above
3 numbers are divisible by all 2, 3 and 5
```

So total numbers divisible by 2, 3 and 5 are =
= 50 + 33 + 20 – 16 – 10 – 6 + 3
= 103 – 29
= 74

So probability that a number is number is not
divisible by 2, 3 and 5 = (100 – 74)/100 = 0.26

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