Catching a cop
Say X has not received a speeding ticket in the last year.
Do the odds that X gets caught speeding tomorrow increase because the event has not occurred during the last year?
Alternately, can A confidently speed tomorrow if he received a ticket today?
Do the odds that X gets caught speeding tomorrow increase because the event has not occurred during the last year?
Alternately, can A confidently speed tomorrow if he received a ticket today?
posted by littlecow at 4/25/2007 07:20:00 PM
7 Comments:
No, the probability does not increased or decreased by the fact that u have got a ticket yesterday, or have not got a ticket for an entire year.
The probability of getting a ticket each time you over speed is independent of whether you were caught the last time :-)
Knowing the deceptive nature of questions on the blog,I'm not sure the above answer is satisfactory,though it seems the most logically sound explanation.
Assuming that no. of cops remain same as the prev year,all have random placements each day, et al., each day's happening is independent of the previous encounters. But how are these cops distributed amongst the road network? Or is it only one single unit working per day?
I agree with above. These are mutually exclusive events.
I see a lot of ways to argue this one, depending on some initial assumptions, but here's one idea: Suppose 1. the police attempt to write a certain number of speeding tickets each day, and that number is lower than the total number of drivers who speed and 2. receiving a second speeding ticket carries a stiffer penalty than the first. Then you would expect those people who have received tickets to drive more slowly, because the expected payoff to speeding is lower for them. Thus, the total pool of speeders is reduced as more people accumulate tickets, and those without tickets are more likely to get caught. But this doesn't really hold up, because if we're going to have people adjust their speeding decisions based on expected payoffs, then the unticketed would slow down as well. Also, this assumes a closed system, with no new reckless teeen drivers emerging.
As for answeres based on how the police are distributed, it's just as reasonable to assume that they frequent certain "hot spots" as it is to say that they're randomly distributed or attempt to cover all locations in a sort of cycle. So without further info that line of thought doesn't satisfy.
Actually, the author just got a ticket and he/she is trying to tap into your collective intellect to see if he/she can safely speed in the near future. I know him/her just too well.
-Shady
Yes, I agree with you all that they are independent events. It is quite likely that the odds of getting a ticket are unchanged between days. But I was interested in whether cops follow the same patterns every day!
Shady: You have read my mind well. But if you did know me well, then you should never have had a he/she confusion. Damn!
madeofplants: I like the way you think. In general, the probability of getting caught is minimized if a speeding driver is sandwiched between two other speeding mates. Also, the chances of being let off the hook during attempts to talk your way out of it are higher in the night than mid-day. But this is not applicable in situations where the cop is hiding and waiting to catch you speeding.
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