Probability of exactly two heads in four coin flips? 
When you flip a coin four times, what is the probability that it will come up heads 
  exactly twice?   

My calculation: 


*

*we have $2$ results for one flip : up or down 

*so flip $4$ times, we have $4\cdot2 = 8$ results total 


Thus the probability is: $2/ 8 = 0.25 $
but the correct answer is $0.375$. Can anyone explain why I'm wrong?
 A: Use binomial probability since there are only two possibilities: success and failure, where success represents getting a heads, and tails being a fail.
Let $X$ = Success (i.e. heads)
Therefore we are trying to find $P(X=2)$, which is $\binom42\cdot(0.5)^2\cdot(0.5)^2=0.375$.
Hope this helped!

The derivation of binomial probability:
Getting two heads out of 4 can be portrayed is, disregarding order:
HHTT (H=heads and T=tails)
Multiplying their probabilities will yield $(0.5)^4$, but as for ordering, we get $4!/(2!\cdot2!)$ due to repetition, which is the same as $4C2$. So our answer is $\binom42\cdot(0.5)^4$ which is $0.375$
A: Assuming unbiased coin with probability of head $=\dfrac12$
and using Binomial Distribution, $$\binom42\left(\frac12\right)^2\left(1-\frac12\right)^{4-2}$$
A: 
My calculation:
we have 2 results for one flip : up or down
  so flip 4 times, we have 4x2 = 8 results total

Two results for each of four coin flips. When ways to perform tasks in series, we multiply.  So that is $2\times 2\times 2\times 2$ results in total. That is $2^4$ or $16$.
For the favourable case we need to count the ways to get $2$ heads and $2$ tails.  The count of permutations of two pairs of symbols is: $\frac{4!}{2!2!}=6$.  This is easily confirmed by just counting.
$$\Bigl|\{\mathsf {HHTT, HTHT, HTTH, THHT, THTH, TTHH}\}\Bigr|=6$$
Thus the probability is: $\tfrac{\;6}{16}$, or: $$0.375$$
A: The generalized answer to r heads in n flips can be calculated this way
The sample space for n space is $2^n$
Number of ways in which you get r heads in n flips is
$nCr = \frac { {n!}}{(n-r)!(r!))} $
So $ P = \frac {{nCr}}{2^n}$
With n = 4 & r = 2
P = 6/16 = 0.375
