Originally Posted by

**ScubaDiver**
There will be two elections. Candidate Heads and candidate tails are running in each election.

Four people vote in each election.

Every voter has a fifty percent chance to vote Heads, and a fifty percent chance to vote tails.

**What is the probability that the election results are identical in each election?**

By "identical" I mean something like this...

One election shows 3 votes for Heads and 1 vote for tails,,,,, and the other election shows 3 votes for Heads and 1 vote for tails.

I thought of this problem yesterday and I think I have an answer. Here is my work.

Possible Cases for a given election

There are 6 50%H 50%T cases

THTH

HTHT

TTHH

HHTT

THHT

HTTH

There are 4 25% T 75% H cases

THHH

HTHH

HHTH

HHHT

There are 4 25% H 75% T cases

HTTT

THTT

TTHT

TTTH

There is 1 100% T case

TTTT

There is 1 100% H case

HHHH

So there are 16 cases total for each election. So I should find the probability that each case would occur in both elections, which could be found by squaring it.

50 50 case = (6/16)(6/16) = 14%

25T 75H case = (1/4)(1/4) = 6.25%

25H 75T case = (1/4)(1/4) = 6.25%

100% H case = (1/16)(1/16) = .39%

100% T case = (1/16)(1/16) = .39%

Then sum the probabilities for the final answer.

**The probability that each election would have the same results is roughly 27.28%.**

Did I make any mistakes in my process here?