5 Every month Susan enters a particular lottery. The lottery company states that the probability, \(p\), of winning a prize is 0.0017 each month. Susan thinks that the probability of winning is higher than this, and carries out a test based on her 12 lottery results in a one-year period. She accepts the null hypothesis \(p = 0.0017\) if she has no wins in the year and accepts the alternative hypothesis \(p > 0.0017\) if she wins a prize in at least one of the 12 months.

1. Find the probability of the test resulting in a Type I error.
2. If in fact the probability of winning a prize each month is 0.0024 , find the probability of the test resulting in a Type II error.
3. Use a suitable approximation, with \(p = 0.0024\), to find the probability that in a period of 10 years Susan wins a prize exactly twice.