+14 1. ) Ava, Lucero, and Vinh are playing a game involving a single -sided die. The rules are as follows:
Ava rolls first. If she rolls a 1, 2 or 3 then she wins.
Otherwise, Lucero rolls next. If Lucero rolls a 4 or a 5 then she wins.
Otherwise, Vinh rolls next. If Vinh rolls a 6 then he wins.
Otherwise, the turn passes back to Ava, with the same rules.
Calculate the probability that Vinh wins.
(A) 1/6 (B) 1/7 (C) 1/8 (D) 1/11 (E) 1/13
+790 The probability of Vinh winning in a single turn is 1/6. The probability of the game not ending in the first two turns is 3/4 * 2/3 = 1/2.
Therefore, the probability of Vinh winning eventually is 1/6 * 1/2 + 1/6 * (1/2)^2 + 1/6 * (1/2)^3 + ...
This is an infinite geometric series with first term 1/12 and common ratio 1/2. The sum of this series is 1/12 * 1/(1-1/2) = 1/6.
Therefore, the probability that Vinh wins eventually is 1/6. The answer is (A).
