   # You are going to flip 8 fair coins and 3 of first four have already landed tails. What is expected total count of tails

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You are going to flip 8 fair coins in total and three of the first four have already landed tails. What do you expect the total count of tails to be when you're finished flipping all 8 coins? posted Jan 9, 2017

expected total count of tails should be independent of the result this far. E(x)=n*mu=8*0.5=4 answer Jan 9, 2017

5 times.
.
The first 4 flips gave 3 tails.
The results of the remaining flips are independent of the first flips, so you would expect half of the remaining flips to give tails (0.5*4=2) (assuming a fair coin).
This gives a total of 3+2 = 5 tails. answer Mar 14, 2017 by

Tricky, tricky....., and very slicky.

The total count of tails (assuming everything is occurring as one event and not separated into 2 events), will trend towards a 50% chance: or 1/2 x 8 = 4.

To assume that the preceding coin tosses have any influence on the next coin toss (or total outcome) is known as "Gambler's Fallacy".

This is also related to the Markov Chain: In probability theory and related fields, a Markov Process, named after the Russian mathematician Andrey Markov, is a type of process that satisfies the Markov property, characterized as being "memorylessness".

Now, if you divide the coin tosses into 2 separate events, then the 2 events are additive. So..., 3 + 2 = 5.

Conclusion: both answers (5 and 4) are correct, as it all depends on your interpretation of this type of "trick" question.

Moral of the story:
Become one of the few,
That can think anew,
And develop a different point of view.

And this is what drives innovation. answer Mar 15, 2017
The 50/50 probability only applies to future tosses. So for the 4 tosses that still need to be made, it is expected that 2 of them would be tail.
For the 4 tosses already made (resulting in 3 tails) nothing will change. Also, the past tosses do not influence the future tosses. Therefore you would expect the total number of tails to be 5 and not 4.

Assuming that the future 4 tosses would only yield 1 tail (making the total tail count 4) would mean that the past tosses influence the future tosses and that is indeed the Gambler's Fallacy.
Interesting analytics. It's always good to get different points of view.

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