Probability, Simulation

2. After giving the lotto a try you decide to go back to Clayton lCampus for some more gambling action. They are playing a die tossing game where you win a brandnew.r home if you roll all sides of the die within T rolls. Your crystal ball can see into the future and tells you that when you roll the die T times you don't see the same number appear twice in a row. You decide to bet your entire rent for the year and try to win the house. You toss a fair sixsided die 7" times. Consider the following events, A = \"each value appears at least once" and B = \"the outcome is alternate in numbers (i.e., a specific face of the die cannot be observed to occur directly after it was observed on the previous roll but it may have occurred elsewhere in the sequence of rolls)\". 'What is p(AlE)? Are you likely to win the house? Solve this analytically (enumeration is not allowed) and experimentally by simulation, in each case printing the T.Falue found