Background Rakel and Lea will organise an engagement reception. They have access to single candles in 4 colors and double candles in 12 other colors to decorate the hall with. A bakery gives them a discount on cakes of two kinds, where they can choose from the very good cakes chocolate cream cake, chocolate nut cake and cream nut cake and from the not so good cake varieties chocolate cake, cream cake and nut cake and from the rather disgusting allergy cake, which contains neither chocolate, cream or nuts. Lea also has a manipulated die, where the probability of getting six is (1/5) and the probability of getting one is (5/36). (Remaining four sides all have the same probability).

To decide who should go out and buy matches to light the candles with, one decide to throw two dice and guess the outcome. Lea exchange the one die for her special die.

1. what is the probability of hitting 9 points with this set of dice, and is it more or less than with normal dice?

2. Rakel actually knew about Lea's special die, and has obtained a similar one, with the one having the highest chance and the six having the lowest. She replaces the normal die with this one. will the probability of hitting 9 now become normal?

3. does the same apply to double-six?