Question 105
Ana, Beto and Carolina will participate in the television program "Discover the color of your hat". In the program, they position themselves in a circle and on the head of each one will be placed a blue or green hat. Everyone can see the hats of others, but not the color of their own hat. Then each of them writes on a paper one of three "blue", "green" or "step" options. If everyone who wrote "blue" or "green" colors hits the color of their hat, they get a car $0 \mathrm{~km}$. If any of them kick the color of the hat, "blue" or "green", and make mistakes, all three lose. If they all write "step", then the three also lose. It is worth mentioning that they cannot combine signals and cannot see the roles of other participants. The three get together to try to combine a strategy. Carolina starts 'None of us should write 'step', we must kick between 'blue' and 'green', because if we all pass, we will lose". 'step'. In this case, the chance of winning will be greater.” Ana pronounces "I had an idea, if we use my strategy we will be likely to $\frac{3}{4}$ to win the car".
(a) Following Carolina's idea, what is the probability of winning the car?
(b) Changing to Beto's idea, what is the probability of winning the car?
(c) Give an example of Ana's possible strategy that makes the probability of winning the car $\operatorname{ser} \frac{3}{4}$.
(a) Following Carolina's idea, what is the probability of winning the car?
(b) Changing to Beto's idea, what is the probability of winning the car?
(c) Give an example of Ana's possible strategy that makes the probability of winning the car $\operatorname{ser} \frac{3}{4}$.