Answer:
a) Ann has a 1/3 chance of winning in the first round
b) The chance of Ann winning for the first time in the fourth round is 8/81
c) The probability that Ann's first win occurs after the fourth round is 16/81
Step-by-step explanation:
a) Each strategy is played with a probability of 1/3. Given any strategy, there’s a 1/3 chance that Bill will choose the strategy that allows Ann to win. Consequently, the probability of Ann securing a victory in the first round (or any round) is
1/3 * 1/3 + 1/3 * 1/3 + 1/3 * 1/3 = 1/9 + 1/9 + 1/9 = 1/3.
Thus, the likelihood of Ann winning the initial round is 1/3.
b) The chances of Ann winning a round stand at 1/3; therefore, her chances of not winning are 2/3. This must happen three times before her first victory. Thus, the probability that Ann's first win occurs in the fourth round is
(2/3)³ * 1/3 = 8/81.
c) The first victory happens after the fourth round if she remains unsuccessful in the first four rounds, translating to a possibility of (2/3)⁴ = 16/81.
Answer:
0.93 minute
Step-by-step explanation:
During the first week:
Kim ran = 1 mile
Duration for this distance = 1 minute
In the second week:
The distance covered by Kim = 1 mile
The time taken by Kim = 7% less compared to the first week
= 1 min - 0.07 min = 0.93 minute
<pSo, she completed 1 mile in 0.93 minute this week.
The correct option is C) $197,263.70. It has decreased 6% annually over the last three years.
