A coin is tossed until sequence HTH appears (H denotes the

Question

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

KarishmaB · Answer

If the game ends after the fourth throw, it means we got either HHTH or THTH. These are the only 2 favorable outcomes. Note, HTHH is not a favorable outcome since in that case the game would end after 3 tosses.
Total possible outcomes with 4 flips of a coin are 2*2*2*2 = 16
Probability of HTH = 2/16 = 1/8

or First flip either H or T is ok. So probability = 1
Second flip, you need H. So probability = 1/2
Third flip, you need T. So probability = 1/2
Fourth flip, you need H. So probability = 1/2
Probability of HTH = 1/2 * 1/2 * 1/2 = 1/8

walkerme13 · Answer

very good explanation

soundofmusic · Answer

Another approach:

Two likely scenarios would be : HHTH or THTH
 for each of the scenarios probability would be 1/16

So Probablilty is 1/16 + 1/16 = 1/8

voodoochild · Answer

Bunuel,
Why aren't we considering  ?   ?    H   T H;  ?   ?   ?    H   T H ..In these cases, the game ends "after" 4 throw. The above explanation would be valid if the question said "The game ends ON the fourth throw"

Essentially, HTH could come on the seventh throw...or on n'th throw...

correct?

Bunuel · Answer

Not correct.

We are told that "a coin is tossed  until  sequence  HTH  appears" and are asked to find "the probability that the game will end after the fourth throw" (so the fourth throw should be the last in the game). After the fourth throw the game will end either in H HTH  or in T HTH  case.

I see no ambiguity here at all.

voodoochild · Answer

Question - What would you call this sequence:

H H H H H H T H ..It's ending  AFTER  4th throw! Isn't it? I am open to your thoughts.

Bunuel · Answer

Again: "the game will end after the fourth throw" means that the fourth throw should be the last in the game.

bumpbot · Answer

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A coin is tossed until sequence HTH appears (H denotes the

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