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

Question

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?

Answer 1

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

Answer 2

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 3

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.

Comments

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.

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Interesting analytics. It's always good to get different points of view.