Probability q (1 Viewer)

[CHUDYMASTER]

I came across this question in the 2001 CSSA trial. It was the very last question.

Basically, you have the vowels in a circular disk and a pointer at the centre is spun. The question is what is the number of turns required to have a 99 % chance of landing on at LEAST one E.

I get the logarthmic aspect, but why have the answers said (4/5)^n = 0.99? Why do they use the complement of E? Could someone explain this in words?

 

[Lazarus]

P(at least one) = 1 - P(none)

The probability of 'at least one' spans the entire range of outcomes except for the outcome of 'none', and hence one is the complement of the other.

They worked out the probability of spinning no E's and found the complement.

 

[CHUDYMASTER]

No, but see that's the thing. Isn't the P(none) = 4/5? Meaning the complement of that is actually 1/5???

 

[Lazarus]

Hmm, yes, it seems then that your answers may contain an error...

P(at least one) >= 0.99
1 - P(none) >= 0.99
1 - (4/5)ⁿ >= 0.99
(4/5)ⁿ >= 0.01

...

n >= 20.6...
n = 21

 

[CHUDYMASTER]

Ahh thanks. Yeah I was worried for a minute there.

 

[Lexicographer]

Haha yeah our maths faculty (as well as my tutor) says the CSSA trals answers are always FULL of mistakes.