A) 1/3
B) 5/21
C) 1/4
D) 2/5
Correct Answer: B
Solution :
[b] Let P(S)=P(1 or 2) = 1/3 P(F) = P (3 or 4 or 5 or 6) = 2/3 P(A wins) = P[SS or S F SS or S F S F SS or ...) Or (F S S or F S F S S or ...)] \[=\frac{\frac{1}{9}}{1-\frac{2}{9}}+\frac{\frac{2}{27}}{1-\frac{2}{9}}\] \[=\frac{1}{9}\times \frac{9}{7}+\frac{2}{27}\times \frac{9}{7}\] \[=\frac{1}{7}+\frac{2}{21}=\frac{3+2}{21}=\frac{5}{21}\] P(A winning)\[=\frac{5}{21}\], P(B winning)\[=\frac{16}{21}\]
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