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        riddles >> medium >> WILLYWUTANG HAS STDS?
        
(Message started by: rugga on Sep 9^th, 2002, 3:34am)

Title: WILLYWUTANG HAS STDS?
Post by rugga on Sep 9^th, 2002, 3:34am

Quote:

While willywutang was trying to be clever by using only two condoms to satisfy three women, increased friction between overlapped latex layers produces a tear and a dangerous accident! He then becomes very worried about having contracted an STD, especially since one of the women was really skanky looking. Although a random person has only probability 0.001 of having an STD, poor willywutang just can't sleep over those odds. Frantically he hustles to the nearest drugstore, to purchase the ACME All-Purpose STD Checker. The packaging boasts a 0.93 correctness probability. That is, if the user has an STD, the ACME STD Checker will return positive 93% of the time; if the user does not have an STD, it will return negative 93% of the time. Willywutang returns home and uses the checker in his bathroom.

To his dismay, the results are positive.

What is the probability that willywutang has STDs?

Trick question! Not to offend Willywutang, but anyone who would attempt to satisfy three women (one really skanky looking) at one sitting :o -- improperly using comdoms to boot -- has a higher chance of having an STD than a "random person". Without getting graphic, Willy's willy may have been exposed to 1, 2, or all 3 of the women depending on when and where the tear occurred:-[ This is not even considering what this event implies about willy's previous (probably impressive) social life.
More seriously, this is one reason why doctors/nurses take a patient's history along with their blood when doing tests. The patient's history gives context for interpreting the test results by way of adjusting the a priori probability for that individual. Of course in real life it's impossible to do this adjustment quantitatively, but it's more information on which to base the necessary human judgement.

Now, if the question concerned billybutane about whom I know nothing, then I could reason as follows...

Using Bayes' rule (see any probablity textbook):

p(STD | positive) = p(STD) p(positive | STD) / p(positive)

= p(STD) p(positive | STD) /
[ p(positive | STD) p(STD) + p(positive | no STD) p(no STD) ]

p(STD) = 0.001 because billy is a random person
p(no STD) = 0.999

p(positive | STD) = 0.93 = success rate of test
p(positive | no STD) = 0.07 = error rate of test

Plugging in the numbers, billybutane finds out ....

only 1.3% chance of STD. He (she?) can relax. Or more accurately, I can relax because I don't know anything about him that might affect the 0.001. Of course he may know something about himself that raises his risk like our poor friend willy.

I suppose another way to approach the question is to consider the chance that willywutang caught an STD during this one encounter, but we really need more information to approach it that way, like the chance of transmitting an STD in one encounter, how many of the three women he was exposed to, whether skanky looking people are more likely to have STDs, etc.

Title: Re: WILLYWUTANG HAS STDS?
Post by Chronos on Sep 11^th, 2002, 7:57pm

I see four or five ways to interpret this problem:

1: The figure of .001 is the a priori probability of Willy having an STD, with all relevant factors considered. In this case, enough information is presented in the problem.

2: The skanky girl had a .001 chance of having an STD, and the other two girls (and, initially Willy) are presumed clean. In this (and following) case(s), we need to know what the probability of disease transmission is.

3: All three girls have a .001 chance of having an STD, but Willy is initially presumed clean. Again, we need to know the transmission probability.

4: Before the encounter, all four people have an a priori .001 chance of having an STD. After the encounter, due to being exposed to each other, they all have probabilities higher than that.

So, Willy, which is it?

Title: Re: WILLYWUTANG HAS STDS?
Post by william wu on Sep 28^th, 2002, 1:46pm

guess i goofed. hehe, sorry guys. ok, to salvage the riddle, i have added the following line:

Quote:

Assuming that willywutang's promiscuity on average is identical to that of a randomly chosen person, what is the probability that willywutang has STDs?

i think this fixes it, but let me know otherwise.

love the sense of humor btw, you guys are the best :)

Title: Re: WILLYWUTANG HAS STDS?
Post by luke's new shoes on Nov 12^th, 2002, 3:50pm

there are two possibilities
1. he has stds and the kit is correct
2. he doesnt have stds and the kit is wrong

probability of 1. is 0.001*0.93 = 0.00093
probability of 2. is 0.999*0.07 = 0.06993

because they are the only two possibilites, their sum must add up to one (well the sum of a common ration of the two must add up to one)

i.e. 0.00093*x + 0.06993*x = 1
(0.00093 + 0.06993)*x = 1
0.07086*x = 1
x = 14.1
therefore probabiltiy of willy having an std is 0.00093*14.1
which equals 0.013