Umm... hi everyone, please don't calculate here. Remember, that's what the writer of the test wants you to do, but it's unnecessary.
The GRE is testing you on what's known as Gambler's Fallacy, or in simpler terms,
the past does not predict the future. No matter what happened during the previous flips, it won't affect
the fourth flip taken in isolation.Go back to the wording of the question: it's specifically
only discussing the fourth flip.
Any given flip taken alone will have a probability of 1/2, therefore the fourth flip has a probability of 1/2.
(Just like the first, second, third, and fifth would if isolated.)
Answer C.
_________________
GRE / GMAT Tutor London and Online since 2005. Writer, editor, contributor for test-prep materials.
Struggling with Permutations and Combinations (Combinatorics?). I've put loads of free resources here:
https://privategmattutor.london/gmat-combinatorics-ultimate-guide-to-gmat-permutations-and-combinations/As ever, feel free to get in touch for impartial GRE / GMAT advice or to enquire about lessons at:
https://privategmattutor.london