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).

- Diet The guests were able to tick on the answer cards if they were hypersensitive to chocolate, cream or nuts. Rakel had begun to compile answers. A total of 23 are hypersensitive to something. 7 are hypersensitive to chocolate, 8 to cream and 14 to nuts, and among them 4 are hypersensitive to both chocolate and nuts while none are hypersensitive to both chocolate and cream. When she got that far she was interrupted, and when she came back someone had thrown the cards away.

1. illustrate the problem with a Venn diagram. 2. Calculate the missing information. 3. Based on this, what two kinds of cake would you recommend they order, and choose?