Two real problems
I pick two reals x and y. I show one of them to you randomly by tossing a fair coin. You have to tell me if the number you see is the larger or the smaller of the two. How do you do this so that for any choice of x and y, the probability that you are correct is strictly larger than .5?
On a sold out flight, 100 people line up to board the plane. The first passenger in the line has lost his boarding pass, but was allowed in, regardless. He takes a random seat. Each subsequent passenger takes his or her assigned seat if available, or a random unoccupied seat, otherwise. What is the probability that the last passenger to board the plane finds his seat unoccupied?
On a sold out flight, 100 people line up to board the plane. The first passenger in the line has lost his boarding pass, but was allowed in, regardless. He takes a random seat. Each subsequent passenger takes his or her assigned seat if available, or a random unoccupied seat, otherwise. What is the probability that the last passenger to board the plane finds his seat unoccupied?
posted by littlecow at 9/28/2006 07:51:00 PM
2 Comments:
manoj: your analysis is perfectly acceptable for a bounded real set but not for the present scenario.
ben: yes and thats what makes the problem difficult!
grenade: alright. you ceil your points.
For the first problem,I have a clarification to be made:
Is only one toss allowed,or multiple tosses?In that case,I'd ask you to keep tossing until the two sides come up,and thus I'd be able to tell you.
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