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by BTGmoderatorRO » Sun Dec 24, 2017 8:48 am
A coin is tossed until sequence HTH appears (H denotes the fall of heads, T denotes the fall of tails). What is the probability that the game will end after the fourth throw?

A. 1/16
B. 3/32
C. 1/8
D. 3/16
E. 1/4

OA is C

Do I need to draw a T-Tree to solve this question? or what could be the best possible option?
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by elias.latour.apex » Sun Dec 24, 2017 10:38 am
Since the first coin toss has no bearing on whether the game will end on the fourth toss, we can ignore it. Our only consideration is what is the probability that the second throw will be heads, the third throw tails, and the fourth throw heads?

There is a 1/2 chance that the second throw will be heads.
There is a 1/2 chance that the third throw will be tails.
There is a 1/2 chance that the fourth throw will be heads.

The chances that all three will occur is (1/2)^3 or 1/8.
Elias Latour
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