SOLUTION: A coin is tossed n times when n>1. Show that the probability of obtaining at least one tail and at least one head is (1-2)^1-n Thank you!

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Question 1003561: A coin is tossed n times when n>1. Show that the probability of obtaining at least one tail and at least one head is (1-2)^1-n
Thank you!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I believe there is a typo in your formula;
(1-2)^1-n=%281-2%29%5E1-n=%28-1%29%5E1-n=-1-n is always a negative number.
(1-2)^(1-n)=%281-2%29%5E%281-n%29=%28-1%29%5E%281-n%29 is 1 half of the times, and -1 the rest of the times.

If you toss a coin n times when n>1, you are tossing a coin more than 1 time,
meaning 2 times, or 3 times, or 4 times, etc.
Unless you get all heads or all tails, you will obtain "at least one tail and at least one head".
The probability of getting all tails is
%281%2F2%29%5En=1%2F2%5En .
The probability of getting all heads is
%281%2F2%29%5En=1%2F2%5En .
The probability of getting all heads or all tails is
1%2F2%5En%2B1%2F2%5En=2%281%2F2%5En%29=2%2F2%5En=1%2F2%5E%28n-1%29=%281%2F2%29%5E%28n-1%29 .
The probability of that not happening,
meaning the probability of obtaining at least one tail and at least one head, is
1-%281%2F2%29%5E%28n-1%29=1-1%2F2%5E%28n-1%29=%282%5E%28n-1%29-1%29%2F2%5E%28n-1%29 .