pretty good scenario, but what about this one...

imagine you grew up the 2nd of 3 brothers in a small suburb. you spent your summers riding your bike to the park and stealing chrome caps off car tires. your oldest brother was many years apart from you and went away to college or died or something. you didn't really know him anyway, and he was a dick to you growing up, so it doesn't really matter. but your younger brother was born with a debilitating mental handicap, and you always saw yourself as his guardian and caretaker. it was tough growing up with him because his affliction could be a burden on you. it was particularly embarrassing when mom would drop y'all off at the mall, and you'd try to talk to some girls in spencer's and they'd get all creeped out by your brother smiling at everything and doing weird shite and they'd be like "what's his problem? is he retarded or something?" and you'd be like "shut up, it's not his fault. come on jason, let's get outta here..." his name was jason btw. so fast forward 40 or 50 years, and both of your parents haven passed away now. you're married and you have kids of your own to take care of. not to mention you only have a modest 3 bedroom house, and 2 of the 3 are already sharing a room. someone needs to take care of jason, but honestly you don't have the money or the time. you decide to take what little inheritance you received from mom and dad to the casino and try to win big and put jason up in a nice home close to you so you can visit him a lot. there's a new game at the casino where they have 3...no, a million cards flipped upside down. one of them is a million dollar grand prize. you can pick any card, then 999,998 incorrect cards are flipped over. you're given the choice to stay with your original 1-in-a-million chance or switch. remember, you're all jason's got, and he's depending on you.

so do you see that you should switch now?

This post was edited on 2/23/15 at 4:35 pm

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Posted by buckeye_vol

Member since Jul 2014

35255 posts

Posted on 2/23/15 at 4:37 pm to link

quote:
no, a million cards flipped upside down. one of them is a million dollar grand prize. you can pick any card, then 999,998 incorrect cards are flipped over. you're given the choice to stay with your original 1-in-a-million chance or switch. remember, you're all jason's got, and he's depending on you.

You switch again. You have a 99.9999% chance of winning if you switch.

Here is the formulation for any scenario from Wikipedia:

quote:
D. L. Ferguson (1975 in a letter to Selvin cited in (Selvin 1975b)) suggests an N-door generalization of the original problem in which the host opens p losing doors and then offers the player the opportunity to switch; in this variant switching wins with probability (N-1)/[N(N-p-1)]. If the host opens even a single door, the player is better off switching, but, if the host opens only one door, the advantage approaches zero as N grows large (Granberg 1996:188). At the other extreme, if the host opens all but one losing door the advantage increases as N grows large (the probability of winning by switching approaches 1 as N grows very large)

This post was edited on 2/23/15 at 4:51 pm

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