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05 Jul 2025, 08:46
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For p: Probability that n(n+1) divisible by 5
- n(n+1) is divisible by 5 if either n or n+1divisible by 5
- So n≡0 mod 5 or n≡4 mod 5
- Each case gives 120 values → total favorable outcomes = 240
- p=240/600=2/5
- n(n−1)divisible by 25 if either n or n−1divisible by 25
- So n≡0 mod 25 or n≡1 mod 25
- Each case gives 24 values → total favorable outcomes = 48
- q=48/600=2/25
Bunuel
20 Jul 2025, 09:24
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Can anyone explain how q = 2/25?
If n(n-1) is divisible by 25, then that means either n or n-1 is divisible by 25.
if n is divisible by 25 -> then there are 24 such numbers.
If n-1 is divisible 25 -> 26, 51, 76, and so on -> 26 + 25x <= 600.
Solving for this we get x <= 22. Including initial 26 as well -> total n-1 numbers divisible by 25 = 23.
So total numbers becomes 47 and not 48.
If n(n-1) is divisible by 25, then that means either n or n-1 is divisible by 25.
if n is divisible by 25 -> then there are 24 such numbers.
If n-1 is divisible 25 -> 26, 51, 76, and so on -> 26 + 25x <= 600.
Solving for this we get x <= 22. Including initial 26 as well -> total n-1 numbers divisible by 25 = 23.
So total numbers becomes 47 and not 48.
21 Jul 2025, 21:22
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you still need to include n=1 because 0 is divisible by 25. This will give you the needed two solutions in every set of 25.
Mrinalsingh13
