Respuesta :
Answer:
a) Ann wins in the first round with probability 1/3
b) The probability that Ann's first win is in the fourth round in 8/81
c) The probability that Ann's first win comes after the fourth round is 16/81
Step-by-step explanation:
a) Each strategy is played with a probability of 1/3. Given each strategy, there is a probability of 1/3 that Bill plays the strategy that makes Ann the winner. Therefore, the probability that Ann wins in the first raound (and, in fact, in any round) is
1/3 * 1/3 + 1/3 * 1/3 + 1/3 * 1/3 = 1/9 + 1/9 + 1/9 = 1/3.
The probability that Ann wins in the first round is 1/3.
b) Ann winning in a round happens with probaiblity 1/3, therefore, she wont win in a round with probability 2/3. This should happen 3 times before the first win, thus, the probability that ann's first win happens in the fourth round is
(2/3)³ * 1/3 = 8/81
c) The first win comes after the fourth found if she doesnt win in the first 4 times, and this will happen with a probability of (2/3)⁴ = 16/81
