Question 60879This question is from textbook
: can u please help me in this
5. person A tosses acoin and then person B rolls adie this is repeated independently until a head or one of the numbers 1,2,3,4 appears, at which time the game is stopped , person A wins with the head and B wins with one of the numbers 1,2,3,4 compute the probability that A wins the game
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A will win with one of the following sequences:
H which has probability 1/2
T,(5 or 6), H which has probability (1/2)(2/6)(1/2)= 1/[6*2]=1/12
T,(5 or 6),T,(5 or 6),H which has probability (1/2)(2/6)(1/2)(2/6)(1/2)
=1/[6^2*2]=1/72
next sequence which has probability 1/[6^3*2]=1/432
then 1/[6*432}=1/2592
etc.
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This gives the series 1/2+1/[6*2]+1/[6^2*2]+...
Sum of this series is (1/2)[(1/6)^(n+1)-1]/[(1/6)-1]
=(1/2)[-1/(-5/6)]=3/5
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So, Probability of A winning is 3/5
Cheers,
Stan H.
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