You can put this solution on YOUR website! Intuition says it should be 0.50, and that is unfortunately incorrect in this case.
There are 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 = 3/8
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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.
