Your Extra Credit

JuanTutors · 2004-08-01, 18:42

You are running a truth test on one randomly chosen object from an infinite sample of objects. Each individual object has the value either TRUE or FALSE (but not both). You happen to know that precisely 1 in every N objects in the sample has value TRUE, while all others have value FALSE. (N can be any positive integer value.) Being a good mathematician, you hardly ever make a mistake. However, no one is perfect and it is true that, on any random test, the probability that you will make a mistake is precisely 1/N.

QUESTION: You ran a your truth test on this one randomly chosen object, and the test came out TRUE. What is the probability that you made a mistake?

wblipp · 2004-08-01, 19:17

My Uncle Laplace used to say, either you're right or you're wrong, so it's 50-50.

In this case he would have been right - it's 50-50.

dsouza123 · 2004-08-01, 21:00

1/N

axn · 2004-08-02, 02:55

I am also going with 50-50

Orgasmic Troll · 2004-08-02, 05:09

50/50

rpresser · 2004-08-30, 05:58

I agree ...

The object is REALLY TRUE with probability 1/N, and REALLY FALSE with probability (N-1)/N. If it is REALLY TRUE (1/N) and I do not make a mistake ((N-1)/N), then I observe a TRUE result with probability (N-1)/(N^2).

On the other hand, if the object is REALLY FALSE ((N-1)/N) and I [U]do[/U] make a mistake (1/N), then I also observe a TRUE result, again with probability (N-1)/(N^2).

Since I did observe a TRUE result, either one of these paths could be true, and since they have equal probabilities, the probability I made a mistake is 50-50.

2004-08-01, 18:42	#1
JuanTutors Mar 2004 7²×11 Posts	Your Extra Credit You are running a truth test on one randomly chosen object from an infinite sample of objects. Each individual object has the value either TRUE or FALSE (but not both). You happen to know that precisely 1 in every N objects in the sample has value TRUE, while all others have value FALSE. (N can be any positive integer value.) Being a good mathematician, you hardly ever make a mistake. However, no one is perfect and it is true that, on any random test, the probability that you will make a mistake is precisely 1/N. QUESTION: You ran a your truth test on this one randomly chosen object, and the test came out TRUE. What is the probability that you made a mistake?

2004-08-02, 02:55	#4
axn Jun 2003 13BC₁₆ Posts	I am also going with 50-50 Last fiddled with by axn on 2004-08-02 at 02:55

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2004-08-01, 19:17	#2
wblipp "William" May 2003 New Haven 2·7·13² Posts	My Uncle Laplace used to say, either you're right or you're wrong, so it's 50-50. In this case he would have been right - it's 50-50.

2004-08-02, 05:09	#5
Orgasmic Troll Cranksta Rap Ayatollah Jul 2003 641₁₀ Posts	50/50

2004-08-30, 05:58	#6
rpresser Jul 2003 2·5 Posts	I agree ... The object is REALLY TRUE with probability 1/N, and REALLY FALSE with probability (N-1)/N. If it is REALLY TRUE (1/N) and I do not make a mistake ((N-1)/N), then I observe a TRUE result with probability (N-1)/(N^2). On the other hand, if the object is REALLY FALSE ((N-1)/N) and I [U]do[/U] make a mistake (1/N), then I also observe a TRUE result, again with probability (N-1)/(N^2). Since I did observe a TRUE result, either one of these paths could be true, and since they have equal probabilities, the probability I made a mistake is 50-50.

2004-08-01, 21:00	#3
dsouza123 Sep 2002 1226₈ Posts	1/N