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A,B,C tosses a coins in turns. The first one to throw a head wins game. What are their respective chances of winning

A,B,C tosses a coins in turns. The first one to throw a head wins game. What are their respective
chances of winning

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
All 3 have a winning sequence WLLL- WLLL,.....
only A's is 1st, 4th, 7th....
B's is 2nd, 5th, 8th.....
C's is 3rd, 6th, 9th.......
in a fair coin, p = q, so
P[A wins] = p + p^4 + p^7 +.... = x (say)
P[B wins] = p^2 + p^5 + p^8 +... = xp
P[C wins] = p^3 + p^6 + p^9 +.... = xp^2
x(1 + p + p^2) = 1
x(1 + 1/2 + 1/4) = 1
x(7/4) = 1
x = 4/7
SoP(A)=4/7
P(B)=2/7
P(C)=1/7
Thanks and Regards
Shaik Aasif
askIITians faculty

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