A number is chosen at random from the set {1, 2, 3, …, 120}. What is the probability that the number chosen is divisible by 6 or 8 but not divisible by 24?
संख्याओं के समुच्चय {1, 2, 3, ..., 120} में से एक संख्या यादृच्छिक रूप से चुनी जाती है। इस बात की प्रायिकता क्या है कि चुनी गई संख्या 6 या 8 से विभाज्य हो, परंतु 24 से विभाज्य न हो?
This Question Asked In:
SSC, CGL, CGL MAINS 2026, CHSL
Correct Answer :B - 5/24
Detailed Text Solution
Total numbers from 1 to 120 = 120.
Numbers divisible by 6 = 120 / 6 = 20.
Numbers divisible by 8 = 120 / 8 = 15.
Numbers divisible by both 6 and 8 are divisible by LCM(6,8) = 24.
Numbers divisible by 24 = 120 / 24 = 5.
Using inclusion-exclusion principle:
Numbers divisible by 6 or 8 = 20 + 15 − 5 = 30.
But we must exclude numbers divisible by 24.
Valid numbers = 30 − 5 = 25.
Required probability = 25 / 120 = 5 / 24.