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comment by mike
mike  ·  938 days ago  ·  link  ·    ·  parent  ·  post: The fake coin probability problem

Just as a pedagogical exercise... you could say that after 4 flips the following are possible:

Real coin

HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT

THHH THHT THTH THTT TTHH TTHT TTTH TTTT

Fake coin

HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH

HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH

Since we know the first three flips are Heads, we eliminate all cases that don't begin with HHH. Tha leaves us:

Real coin:

HHHH HHHT

Fake coin:

HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH

HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH

There are 18 possibilities. 17 of them have Heads on the 4th flip. P(H on 4th) = 17/18.

Same as what you did, but a little more direct.