Today David fixed a big breakfast for us, I did a little laundry and fixed roast chicken for dinner, but basically we’ve had a day of rest, and I’ve been commuting mentally (my usual armchair travel) between northern Michigan and southern Louisiana. The sun was out for a while, air warm, and Sarah and I had a good ramble in the fields. Afterward she was content to lie on the rug and work over a big rawhide bone while David enjoyed ROAD FEVER, by Tim Cahilll, and I lost myself in James Lee Burke’s CRUSADER’S CROSS. More another day about the allure of murder mysteries in romantic places and the back-and-forth from violent crime to pastoral Eden.My picture today is from the last February sunset. But now, it’s March, oh, it’s March! Only three weeks to the spring equinox! But did yesterday count as a lion or a lamb? And let’s not forget that it’s April, not March, that is the cruelest month. The perfection of May and June are nearer than they were but still a long, chilly, snowy, rainy, windy, muddy way off.
As for the probability problem, Ben W. thought it made a difference that the game show host knows where the prize is, but I don't see why. As long as the door he opens is not the door with the prize, so that the contestant has a chance to stick with his first choice or switch doors, how would the host’s knowledge affect the odds, any more than the odds are affected (not at all) by the lack of knowledge of the second competitor I introduced after the third door was eliminated? After all, if you’re betting on a racehorse, the odds for that horse in that race are what they are, whether you know the odds or not.
At least the problem has animated coffee conversation at the Treasure Chest this past week, and what with ever-new topics to chew over and Donna’s cheerful welcome and good breakfasts (the home-fried potatoes warm body and spirit these blustery days), Northport will make it through to spring. But then, we always do.
P.S. I’ve been asked about winter carnival, specifically about the outhouse race. There were five outhouses in competition this year, and if you go to the Chamber of Commerce site (in the links list) you can click from there to a site with videos. Sally Coohon, President of the Northport-Omena Chamber of Commerce, thought there were about 500 participants at this year’s winter carnival.
4 comments:
Glad to find this blog. That is a very chilly-looking winter picture.
Always good to have a new reader. What brought you? Were you drawn by probability?
I think it is crucial that the host knows where the big prize is, but I agree it should not change the probabilities at all.
If the host does not know where the prize is, then the host might accidentally open the door that hides it. That would have the effect of spoiling that instance of the game, as the contestant then knows that he does not have the big prize, and has no reason to think about whether he should switch or not. So, instead of Monty then saying "do you want to switch" and the audience having the fun of trying to figure out what they'd do, and of influencing the contestant, the game is simply over.
The probabilities stayed the same, though.
And note that Monty would normally open one of the unchosen doors whether the contestant had chosen the right door or not. There's no guarantee that by switching the contestant will win the big prize, just twice as big a chance that he will. But 1/3 of the time (on average) switching will cause him to lose.
A local acquaintance drew up a chart, like a truth table for logic, that makes this all crystal clear at a glance. At least I think so until Larry and Maiya still aren't buying, even with the chart, and then my own firm grasp weakens again. With luck I'll see Bob again in the next few days and ask him if I can post his chart.
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