G C S E Code Question

[kuiperbelt]

Liam is trying to remember a 3-digit code.

He knows the rule that, the first digit is a cube number.
The second digit is a factor of 16. The third digit is an odd number.

Liam tries a random code that matches the rule.
Expressing as a percentage, calculate
the probability that his code is correct.

[Zacs-Master]

1 in 40.

[bobbinwales]

well you need to know whether theres 999 or 1000 codes available.
if 000 is allowed thats 1000
Its also affects the numbe rof cubes options because you could include 0 as a cube number alongside 1,8, 27 ect

[bobbinwales]

Sorry its first digit so thats just 0,1,8

[TheWinner]

1st digit 1 or 8
2nd digit (factor of 16) 1 2 4 or 8
3rd digit 1 3 5 7 or 9
= 2 x 4 x 5 variants
= 1/40

[TheWinner]

Zacs-Master wins for being so speedy. . .

[bobbinwales]

011 013 015 017 019
021 023 025 027 029
041 043 045 047 049
081 083 085 087 089

111 113 115 117 119
121 123 125 127 129
141 143 145 147 149
181 183 185 187 189

811 813 815 817 819
821 823 825 827 829
841 843 845 847 849
881 883 885 887 889


so 60 in 1000???

[bobbinwales]

so 1 in 60

[bobbinwales]

there are 60 combos possible of 0 is counted as a cube number (0 x 0 x0)???
Its only 40 if you dont count 0 as a cube

[Togo]

2.5%

[bhg481]

Come on Zacs - read the question again and correct your answer!

[bhg481]

Togo has done it for you.

[bobbinwales]

Yes 2.5% .... if we'er excluding 0 as a cube number. If 0 is counted then its 1.666 recuring% . I seem to be outvoted though so fair enough. See what kuiperbelt thinks

[Zacs-Master]

You're ok thanks. I'm sticking. I think there's some 'over thinking' going on.

[Togo]

Haha. The thread is almost AB in microcosm. A question is "asked" and almost instantly taken up by posters looking to answer first and doing all the number crunching, but omitting to read the fine detail in the question. Another poster over thinking the question and although "technically" right in some aspect of this unnecessary diversion also missing the salient aspect. Then a smug, smart arris, poster(me) with an open goal.

[Togo]

Snap on that point Zacs. I was writing as you posted. :))

[bobbinwales]

overthinking.... better than underthinking? I gave both bpossible answers TOGO including one you say was "technically2 right but dismiss it?? Why???
Thats typical AB!

[Zacs-Master]

If you Google the question the generally accepted answer is 1 in 40.

[Togo]

Did you google the question Zacs?

[Zacs-Master]

I'll leave you to wonder.

[Tuvok]

50%

Its either right or wrong.