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Twenty seven words put B first and G third, and the BEG opening takes more than a third. Every second letter here is a vowel.
E takes the second box in ten of the twenty seven, thirty seven percent. BEGIN, BEGAN, BEGUN, BEGET and BEGOT are the ordinary words in it, and all of them come off the same short stem.
I and O take six words each, giving BIGOT, BIGHT, BOGUS, BOGEY and BOGIE. A takes three with BAGEL and BAGGY, and U takes two with BUGLE and BUGGY. Those branches hold fewer words but more variety, and BAGEL, BUGLE and BOGUS between them test three different vowels.
Four words repeat the G, giving BAGGY, BIGGY, BOGGY and BUGGY. They all end in Y and differ only in the second box, so a visible double plus a Y narrows the page to a single vowel question.
It is the most common word here and it tests the largest branch. If the second letter comes back as something other than E, the remaining page is short enough to read.
No. A bogey is a golf score or a spectre, a bogie is a wheeled undercarriage. Both are on this list and they differ only in the fourth box.
A G in the third box needs a vowel in front of it at five letters. No consonant fits there, which is why the second box has so few options.