Step 1: For the initial 3 coins flipped, Monday and Tuesday each have exactly one success in 8 possible. Step 2: Correctly not singling out a success or failure so far, each of the 8 possible “lookeahead outcome” has an exact 1-1 correspondence between days.

So there is no bias, they have equal chances, and the correct answer is in fact not even offered: “Tuesday could be higher or lower with about equal chances.” We’d need to know the number of flips on each day and the help of a professional statistician to tell us the chances of the 2 days being exactly equal (quite slim, in my opinion).

Specifically, the “explanation” says that for Tuesday’s failure with HTT, “you are one-third of the way to achieving it again.” It ignores that for Monday’s success with HTH, you are one-third of the way to achieving it again, too!

Monday:
HTT – one failure. 0 steps toward a success.
HTH – one success. 1 step toward a success.

Tuesday:
HTH – one failure. 1 step toward a success.
HTT – one success. 0 steps toward a success.

See how these balance out? The writer only considered the first outcome for each day of these four possibilities.

For a deeper analysis of all outcomes, see http://forum.lessthandot.com/viewtopic.php?f=102&t=7271&p=36926#p36926

“Turn on the first switch and leave it on for a few minutes.” → you forgot to say “and then turn it off.”