6 At the last election, 70\% of people in Apoli supported the president. Luigi believes that the same proportion support the president now. Maria believes that the proportion who support the president now is \(35 \%\). In order to test who is right, they agree on a hypothesis test, taking Luigi's belief as the null hypothesis. They will ask 6 people from Apoli, chosen at random, and if more than 3 support the president they will accept Luigi's belief.

1. Calculate the probability of a Type I error.
2. If Maria's belief is true, calculate the probability of a Type II error.
3. In fact 2 of the 6 people say that they support the president. State which error, Type I or Type II, might be made. Explain your answer.