4 ms·

I believe your analysis is incorrect. There is a 50% chance the other line will move faster. With no additional new information, once you've chosen a line to

I believe your analysis is incorrect. There is a 50% chance the other line will move faster. With no additional new information, once you've chosen a line to stand in, the probability you chose the slower line has not changed.

Retric 11y ago
That's after 1 cycle. Assume you chose once per week for 10 years = 520 trips. So, 50% of your trips (260) you would pick the fast lane and 50% of the trips you would pick the slow lane (260). The sum of your slow trip time is 20 * 260 = 5,200 minutes and your fast trip time takes 10 * 260 = 2,600 minutes. So, out of a total wait time of 5200+2600= (7,800) minutes you spent 2/3 of it in the slow lane and 1/3 of it in the fast lane.
- Nadya 11y ago
  I think the last statement of the parent is causing the confusion. >On average now 67% of the time the other line will move faster. This should be: "On average, you spend 67%~ of your time in the slower lane." On average the other lane is still only faster 50% of the time assuming the odds are truly 50/50 - but you spend 67% more time in the slower lane.
  - JoeAltmaier 11y ago
    Gotta be careful with the word 'time'. 50% of your trips, the other lane is faster. 67% of the time, its faster.
- yequalsx 11y ago
  But this isn't what the parent wrote. I think it is what he/she meant but it isn't what was written. The probability that the other lane is faster is still 50%.
  - deleted 11y ago
    [deleted]
wlesieutre 11y ago
There's a 50% chance of a given lane being the fast one, but you'll spend twice as long in the slow lane if you're stuck there. Thinking of total time for grocery store lines may feel unnatural, but it's certainly the perspective that makes sense on a road. I wouldn't start a 200 mile trip by saying "I'm going to spend this trip in the right lane," I'd do some of my driving in each. And if I drive 100 miles in the fast lane and 100 miles in the slow lane, I'll have spent >50% of my time in the slow lane, even if my odds of picking the right one are 50/50 at any given moment.

Retric 11y ago

That's after 1 cycle. Assume you chose once per week for 10 years = 520 trips. So, 50% of your trips (260) you would pick the fast lane and 50% of the trips you would pick the slow lane (260). The sum of your slow trip time is 20 * 260 = 5,200 minutes and your fast trip time takes 10 * 260 = 2,600 minutes. So, out of a total wait time of 5200+2600= (7,800) minutes you spent 2/3 of it in the slow lane and 1/3 of it in the fast lane.

Nadya 11y ago
I think the last statement of the parent is causing the confusion. >On average now 67% of the time the other line will move faster. This should be: "On average, you spend 67%~ of your time in the slower lane." On average the other lane is still only faster 50% of the time assuming the odds are truly 50/50 - but you spend 67% more time in the slower lane.
- JoeAltmaier 11y ago
  Gotta be careful with the word 'time'. 50% of your trips, the other lane is faster. 67% of the time, its faster.
yequalsx 11y ago
But this isn't what the parent wrote. I think it is what he/she meant but it isn't what was written. The probability that the other lane is faster is still 50%.
- deleted 11y ago
  [deleted]

wlesieutre 11y ago

There's a 50% chance of a given lane being the fast one, but you'll spend twice as long in the slow lane if you're stuck there. Thinking of total time for grocery store lines may feel unnatural, but it's certainly the perspective that makes sense on a road. I wouldn't start a 200 mile trip by saying "I'm going to spend this trip in the right lane," I'd do some of my driving in each. And if I drive 100 miles in the fast lane and 100 miles in the slow lane, I'll have spent >50% of my time in the slow lane, even if my odds of picking the right one are 50/50 at any given moment.