10 Apr 08
Originally posted by mtthwYes, that is correct. The problem with the test is that the number of false positives completely swamps out the number of true positives.
1 in 50506. You must be missing one small step.
Remember the sample space is all those that would test positive. So it would be:
99/(99 + 4999995)
What happens if you run the test twice?
10 Apr 08
Originally posted by PBE6The answer to that question would depend on how consistent the test is. If the test had 100% consistency, you would always get the same result, regardless of whether the person had the disease or not.
Yes, that is correct. The problem with the test is that the number of false positives completely swamps out the number of true positives.
What happens if you run the test twice?
Presumably the false positives are caused by some other condition which "mimics" the disease in the component which the test tests for.
In short, I would ask this question. How dependent (or linked) is the second result on the first result?
10 Apr 08
Originally posted by PBE6To reply to the question first posted:
This one comes from the Old West, apparently.
A man with a hat shows you 3 cards, one completely gold, one completely silver, and one gold on one side and silver on the other. He puts them in his hat, and picks one at random. He then shows you one side of the card he picked, which happens to be silver. Now he says "I'll bet you even money that the other side of this card is silver too...whaddaya say, partner?"
Is this bet a fair one?
It is a fair bet. Counting the number if sides is incorrect because sides are not distinct events. The chance of whether the side coming up silver or gold has already been removed from the equation. You are only dealing with 2 bars now.
Saying, "Even money that the other side is silver too" can also be stated "even money that this bar is the all-silver bar" OR "even money that this bar is the two-sided bar". Two possible questions, one or the other is right, 50/50 chance. That's a fair bet and I'd take it.
10 Apr 08
Originally posted by broblutoYou're right that you're choosing between two cards, but the wrinkle is that one card comes up silver 1/2 the time (the silver/gold card) and one comes up silver 2/2, or all the time (the silver/silver card).
To reply to the question first posted:
It is a fair bet. Counting the number if sides is incorrect because sides are not distinct events. The chance of whether the side coming up silver or gold has already been removed from the equation. You are only dealing with 2 bars now.
Saying, "Even money that the other side is silver too" can also be stated "even ...[text shortened]... e questions, one or the other is right, 50/50 chance. That's a fair bet and I'd take it.
If you don't believe me, try running the game yourself. Take 3 playing cards, and place stickers on both sides of each card with labels such that you create a gold/gold card, a silver/gold card and a silver/silver card. If a silver side is shown, always bet that the other side is silver too and record the results. (If the gold/gold card comes up, record that fact but disregard for betting purposes. Alternatively, change the bet so that you bet the other side is gold, too.)
10 Apr 08
Originally posted by broblutoNo.
To reply to the question first posted:
It is a fair bet. Counting the number if sides is incorrect because sides are not distinct events. The chance of whether the side coming up silver or gold has already been removed from the equation. You are only dealing with 2 bars now.
Saying, "Even money that the other side is silver too" can also be stated "even ...[text shortened]... e questions, one or the other is right, 50/50 chance. That's a fair bet and I'd take it.
Wow, this question just refuses to die! I guess you picked a good one, PBE6.
10 Apr 08
Originally posted by PBE6Forget about sides. Your confusing the point.
You're right that you're choosing between two cards, but the wrinkle is that one card comes up silver 1/2 the time (the silver/gold card) and one comes up silver 2/2, or all the time (the silver/silver card).
If you don't believe me, try running the game yourself. Take 3 playing cards, and place stickers on both sides of each card with labels such that you ...[text shortened]... etting purposes. Alternatively, change the bet so that you bet the other side is gold, too.)
Fact 1: He has one card in his hand
Fact 2: That card is 1 of 2 possible cards.
Outcome 1: It is the right card
Outcome 2: It is the wrong card.
50/50 chance.
10 Apr 08
Originally posted by broblutoNo. Think about it this way, brobluto. It is supposed that you have chosen one side randomly. Now, given the additional information that this side happens to be silver, do you not see how it is twice as likely that this side belongs to the silver/silver bar than the silver/gold bar?
Forget about sides. Your confusing the point.
Fact 1: He has one card in his hand
Fact 2: That card is 1 of 2 possible cards.
Outcome 1: It is the right card
Outcome 2: It is the wrong card.
50/50 chance.
10 Apr 08
Originally posted by LemonJelloNo. It's not. If you have only two bars in the hat, silver/silver and silver/gold, then the chances that you bring out a silver facing side is 3 in 4 (75😵 chance. The chance that you bring out the silver/silver bar is 1 in 2 (50😵 and the chance that it's the silver/gold is 1 in 2 (50😵.
No. Think about it this way, brobluto. It is supposed that you have chosen one side randomly. Now, given the additional information that this side happens to be silver, do you not see how it is twice as likely that this side belongs to the silver/silver bar than the silver/gold bar?
10 Apr 08
Originally posted by broblutoLemonJello is right about this one. I recommend running the game yourself and checking the results. I think you'll be surprised.
No. It's not. If you have only two bars in the hat, silver/silver and silver/gold, then the chances that you bring out a silver facing side is 3 in 4 (75😵 chance. The chance that you bring out the silver/silver bar is 1 in 2 (50😵 and the chance that it's the silver/gold is 1 in 2 (50😵.
10 Apr 08
3 edits
Originally posted by broblutoExactly. So there are three cases when you bring out silver side. And only in one case the other side can be golden.
If you have only two bars in the hat, silver/silver and silver/gold, then the chances that you bring out a silver facing side is 3 in 4 (75😵 chance.
EDIT: Look at it this way. You can't see the whole card, you see only a side, so you have to consider the number of sides, not cards. And there are three silver sides, where to only one of them, the reverse is golden.