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probability calculation given information
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I thought I had the hang of probabilities and conditional probabilities but then this question confused me. It all started with the following tweet:
'I was driving in an empty road at night when a guy signaled for a ride. He got on and after a while asked me "didn't it occur to you that I could be a serial killer?" I answered, "no, because the probability of a serial killer meeting a serial killer is astronomically small"'
The implication is that the driver (the author of the tweet) is a serial killer.
This tweet sparked an argument among my friends. There were two arguments.
One group said that, the author's argument is correct. That the probability of the guy getting in is a serial killer is low given that the driver himself is a serial killer.
The other group said that, the author's argument is incorrect. The probability of the passenger being a serial killer is independent of the fact that the driver is a serial killer. So the probability of the guy getting in is a serial killer doesn't change.
Now I'm totally confused and feel like I haven't really grasped the concept of probabilities and conditional probabilities. Which argument is true? And why?
Any help would be appreciated.
probability
asked Jul 28 at 20:39
PPGoodMan
617
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up vote
0
down vote
favorite
I thought I had the hang of probabilities and conditional probabilities but then this question confused me. It all started with the following tweet:
'I was driving in an empty road at night when a guy signaled for a ride. He got on and after a while asked me "didn't it occur to you that I could be a serial killer?" I answered, "no, because the probability of a serial killer meeting a serial killer is astronomically small"'
The implication is that the driver (the author of the tweet) is a serial killer.
This tweet sparked an argument among my friends. There were two arguments.
One group said that, the author's argument is correct. That the probability of the guy getting in is a serial killer is low given that the driver himself is a serial killer.
The other group said that, the author's argument is incorrect. The probability of the passenger being a serial killer is independent of the fact that the driver is a serial killer. So the probability of the guy getting in is a serial killer doesn't change.
Now I'm totally confused and feel like I haven't really grasped the concept of probabilities and conditional probabilities. Which argument is true? And why?
Any help would be appreciated.
probability
asked Jul 28 at 20:39
PPGoodMan
617
3
I know this "argument" in the form that you should always carry a bomb with you on an airplane, because the probability of there being two bombs on the same plane is so low :-)
– joriki
Jul 28 at 20:55
1
I also have no idea about dependence of such crimes. Maybe there is some law or criminology or statistics StackExchange you can look for. Most things with human behaviour is very dependent on circumstances. We act and react. We joke and we respond to jokes. Or maybe with some probability we don't get that the joke was a joke and so on.
– mathreadler
Jul 28 at 20:58
1
@joriki I see your point. I think I managed to clean up the point now. I was confused about the probability of driver and passenger both being serial killers (which is actually low) and passenger being a criminal given that the driver is a serial killer. But I'm still not sure which probability should I apply when I as a serial killer, see a man signaling for a ride.
– PPGoodMan
Jul 28 at 21:17
@mathreadler my question wasn't about dependence of crimes or human behaviour though. It was a confusing point in maths. I think I figured it out. Please see my previous comment and let me know if my understanding is wrong.
– PPGoodMan
Jul 28 at 21:19
@PPGoodMan, I think that your explanation about your confusion is a good one. If you are a serial killer, then that is given information, and so can (and probably should) be used to evaluate the relevant probability as a conditional probability.
– LSpice
Jul 29 at 19:59
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I thought I had the hang of probabilities and conditional probabilities but then this question confused me. It all started with the following tweet:
'I was driving in an empty road at night when a guy signaled for a ride. He got on and after a while asked me "didn't it occur to you that I could be a serial killer?" I answered, "no, because the probability of a serial killer meeting a serial killer is astronomically small"'
The implication is that the driver (the author of the tweet) is a serial killer.
This tweet sparked an argument among my friends. There were two arguments.
One group said that, the author's argument is correct. That the probability of the guy getting in is a serial killer is low given that the driver himself is a serial killer.
The other group said that, the author's argument is incorrect. The probability of the passenger being a serial killer is independent of the fact that the driver is a serial killer. So the probability of the guy getting in is a serial killer doesn't change.
Now I'm totally confused and feel like I haven't really grasped the concept of probabilities and conditional probabilities. Which argument is true? And why?
Any help would be appreciated.
probability
asked Jul 28 at 20:39
PPGoodMan
617
I thought I had the hang of probabilities and conditional probabilities but then this question confused me. It all started with the following tweet:
'I was driving in an empty road at night when a guy signaled for a ride. He got on and after a while asked me "didn't it occur to you that I could be a serial killer?" I answered, "no, because the probability of a serial killer meeting a serial killer is astronomically small"'
The implication is that the driver (the author of the tweet) is a serial killer.
This tweet sparked an argument among my friends. There were two arguments.
One group said that, the author's argument is correct. That the probability of the guy getting in is a serial killer is low given that the driver himself is a serial killer.
The other group said that, the author's argument is incorrect. The probability of the passenger being a serial killer is independent of the fact that the driver is a serial killer. So the probability of the guy getting in is a serial killer doesn't change.
Now I'm totally confused and feel like I haven't really grasped the concept of probabilities and conditional probabilities. Which argument is true? And why?
Any help would be appreciated.
probability
asked Jul 28 at 20:39
PPGoodMan
617
asked Jul 28 at 20:39
PPGoodMan
617
asked Jul 28 at 20:39
PPGoodMan
617
asked Jul 28 at 20:39
PPGoodMan
617
617
3
I know this "argument" in the form that you should always carry a bomb with you on an airplane, because the probability of there being two bombs on the same plane is so low :-)
– joriki
Jul 28 at 20:55
1
I also have no idea about dependence of such crimes. Maybe there is some law or criminology or statistics StackExchange you can look for. Most things with human behaviour is very dependent on circumstances. We act and react. We joke and we respond to jokes. Or maybe with some probability we don't get that the joke was a joke and so on.
– mathreadler
Jul 28 at 20:58
1
@joriki I see your point. I think I managed to clean up the point now. I was confused about the probability of driver and passenger both being serial killers (which is actually low) and passenger being a criminal given that the driver is a serial killer. But I'm still not sure which probability should I apply when I as a serial killer, see a man signaling for a ride.
– PPGoodMan
Jul 28 at 21:17
@mathreadler my question wasn't about dependence of crimes or human behaviour though. It was a confusing point in maths. I think I figured it out. Please see my previous comment and let me know if my understanding is wrong.
– PPGoodMan
Jul 28 at 21:19
@PPGoodMan, I think that your explanation about your confusion is a good one. If you are a serial killer, then that is given information, and so can (and probably should) be used to evaluate the relevant probability as a conditional probability.
– LSpice
Jul 29 at 19:59
add a comment |Â
3
I know this "argument" in the form that you should always carry a bomb with you on an airplane, because the probability of there being two bombs on the same plane is so low :-)
– joriki
Jul 28 at 20:55
1
I also have no idea about dependence of such crimes. Maybe there is some law or criminology or statistics StackExchange you can look for. Most things with human behaviour is very dependent on circumstances. We act and react. We joke and we respond to jokes. Or maybe with some probability we don't get that the joke was a joke and so on.
– mathreadler
Jul 28 at 20:58
1
@joriki I see your point. I think I managed to clean up the point now. I was confused about the probability of driver and passenger both being serial killers (which is actually low) and passenger being a criminal given that the driver is a serial killer. But I'm still not sure which probability should I apply when I as a serial killer, see a man signaling for a ride.
– PPGoodMan
Jul 28 at 21:17
@mathreadler my question wasn't about dependence of crimes or human behaviour though. It was a confusing point in maths. I think I figured it out. Please see my previous comment and let me know if my understanding is wrong.
– PPGoodMan
Jul 28 at 21:19
@PPGoodMan, I think that your explanation about your confusion is a good one. If you are a serial killer, then that is given information, and so can (and probably should) be used to evaluate the relevant probability as a conditional probability.
– LSpice
Jul 29 at 19:59
3
3
I know this "argument" in the form that you should always carry a bomb with you on an airplane, because the probability of there being two bombs on the same plane is so low :-)
– joriki
Jul 28 at 20:55
I know this "argument" in the form that you should always carry a bomb with you on an airplane, because the probability of there being two bombs on the same plane is so low :-)
– joriki
Jul 28 at 20:55
1
1
I also have no idea about dependence of such crimes. Maybe there is some law or criminology or statistics StackExchange you can look for. Most things with human behaviour is very dependent on circumstances. We act and react. We joke and we respond to jokes. Or maybe with some probability we don't get that the joke was a joke and so on.
– mathreadler
Jul 28 at 20:58
I also have no idea about dependence of such crimes. Maybe there is some law or criminology or statistics StackExchange you can look for. Most things with human behaviour is very dependent on circumstances. We act and react. We joke and we respond to jokes. Or maybe with some probability we don't get that the joke was a joke and so on.
– mathreadler
Jul 28 at 20:58
1
1
@joriki I see your point. I think I managed to clean up the point now. I was confused about the probability of driver and passenger both being serial killers (which is actually low) and passenger being a criminal given that the driver is a serial killer. But I'm still not sure which probability should I apply when I as a serial killer, see a man signaling for a ride.
– PPGoodMan
Jul 28 at 21:17
@joriki I see your point. I think I managed to clean up the point now. I was confused about the probability of driver and passenger both being serial killers (which is actually low) and passenger being a criminal given that the driver is a serial killer. But I'm still not sure which probability should I apply when I as a serial killer, see a man signaling for a ride.
– PPGoodMan
Jul 28 at 21:17
@mathreadler my question wasn't about dependence of crimes or human behaviour though. It was a confusing point in maths. I think I figured it out. Please see my previous comment and let me know if my understanding is wrong.
– PPGoodMan
Jul 28 at 21:19
@mathreadler my question wasn't about dependence of crimes or human behaviour though. It was a confusing point in maths. I think I figured it out. Please see my previous comment and let me know if my understanding is wrong.
– PPGoodMan
Jul 28 at 21:19
@PPGoodMan, I think that your explanation about your confusion is a good one. If you are a serial killer, then that is given information, and so can (and probably should) be used to evaluate the relevant probability as a conditional probability.
– LSpice
Jul 29 at 19:59
@PPGoodMan, I think that your explanation about your confusion is a good one. If you are a serial killer, then that is given information, and so can (and probably should) be used to evaluate the relevant probability as a conditional probability.
– LSpice
Jul 29 at 19:59
add a comment |Â
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3
I know this "argument" in the form that you should always carry a bomb with you on an airplane, because the probability of there being two bombs on the same plane is so low :-)
– joriki
Jul 28 at 20:55
1
I also have no idea about dependence of such crimes. Maybe there is some law or criminology or statistics StackExchange you can look for. Most things with human behaviour is very dependent on circumstances. We act and react. We joke and we respond to jokes. Or maybe with some probability we don't get that the joke was a joke and so on.
– mathreadler
Jul 28 at 20:58
1
@joriki I see your point. I think I managed to clean up the point now. I was confused about the probability of driver and passenger both being serial killers (which is actually low) and passenger being a criminal given that the driver is a serial killer. But I'm still not sure which probability should I apply when I as a serial killer, see a man signaling for a ride.
– PPGoodMan
Jul 28 at 21:17
@mathreadler my question wasn't about dependence of crimes or human behaviour though. It was a confusing point in maths. I think I figured it out. Please see my previous comment and let me know if my understanding is wrong.
– PPGoodMan
Jul 28 at 21:19
@PPGoodMan, I think that your explanation about your confusion is a good one. If you are a serial killer, then that is given information, and so can (and probably should) be used to evaluate the relevant probability as a conditional probability.
– LSpice
Jul 29 at 19:59