Question 1108079
Intuition says it should be  0.50, and that is unfortunately incorrect in this case.

There are {{{ 2^4 = 16 }}} possible outcomes.

Breaking it down into groups of two:

HH  —> Only TT can follow this
HT  —>  Only HT or TH can follow this
TH   —>  Only HT or TH can follow this 
TT  —>  Only HH can follow this

So out of 16 possible outcomes, only 6 have exactly two heads and two tails.  

The probability of getting two heads and two tails is then  6/16 = <b>3/8</b>

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An alternative way to look at this: there are 4 slots for each of the 4 flips, and we want heads to occupy exactly 2 of them:  C(4,2) = 4!/(2!*2!) = 24/4 = 6,  and dividing by the 16 possible outcomes, that computes to a probability of 6/16 = 3/8.