A fair coin with faces 0 and 1 is tossed repeatedly to see whether the ordered triple 111 or 011 turns up first. What is the probability that 111 will turn up first?
2007-01-08 13:35:57 · 7 answers · asked by ItalianStallion 2 in Science & Mathematics ➔ Mathematics
The chances that the coin turns up 1 is 1/2. So the chances that it turns up 111 is 1/2 X 1/2 X 1/2 = 1/8.
Likewise the chances that it turns up 011 is also 1/8.
2007-01-08 13:42:44 · answer #1 · answered by vach1970 2 · 0⤊ 1⤋
It looks as if 011 and 111 are as likely to turn up first, but they aren't (that would be true only if one considers "blocks" of 3 tosses).
The only case where 111 will turn up first is if the FIRST three tosses are 1. Otherwise, there is at least a 0 somewhere in the sequence and once cannot get a 111 without encountering a 011 before (the best way to see it is by contradiction).
And the probability to get 111 at the beginning is 1/8.
2007-01-09 01:34:26 · answer #2 · answered by chaps 2 · 0⤊ 0⤋
1/8
2007-01-08 21:39:55 · answer #3 · answered by arthur!!! 4 · 0⤊ 0⤋
Since all outcomes are equally likely the probability is 1/2
2007-01-08 21:39:07 · answer #4 · answered by hayharbr 7 · 0⤊ 0⤋
It's not 1/2. It seems like it should be, but it's not. I can't remember how to solve it, but the method depends on Markov Chains.
2007-01-08 23:48:10 · answer #5 · answered by MathGuy 3 · 0⤊ 0⤋
1/2 you are equally likely to get both answers.
2007-01-08 21:40:10 · answer #6 · answered by jforrest46221 2 · 0⤊ 0⤋
why don't you do your own homework?
2007-01-08 21:39:50 · answer #7 · answered by ShaLaLaLaLaLaMyOhMy 4 · 0⤊ 1⤋