3 Sumitra has a six-sided die. She suspects that it is biased so that it shows a six less often than it would if it were fair. She decides to test the die by throwing it 30 times and noting the number of throws on which it shows a six.

1. It shows a six on exactly 2 throws. Use a binomial distribution to carry out the test at the \(5 \%\) significance level.
2. Later, Sumitra repeats the test at the \(5 \%\) significance level by throwing the die 30 times again. Find the probability of a Type I error in this second test.