For breakfast Bob has three options: cereal, eggs or fruit. He has to choose exactly two items out of the three available. (a) Describe the sample space of this experiment. Hint. What are the different possible outcomes for Bob's breakfast? (b) Let A be the event that Bob's breakfast includes cereal. Express A as a subset of the sample space.

Step-by-step explanation:

The same space of this experiment is the possible outcomes of selecting two out of the three breakfast. let the sample space = B

the sample space = { (cereal and egg), (cereal and fruit), (fruit and egg), (fruit and cereal), (egg and fruit), (egg and cereal) }

b) A = { (cereal and egg), (cereal and fruit), (egg and cereal), (fruit and cereal) }

A ⊆ B = n (A) ≤ n (B) (4≤6) = { (cereal and egg), (cereal and fruit), (egg and cereal), (fruit and cereal) } ⊆{ (cereal and egg), (cereal and fruit), (fruit and egg), (fruit and cereal), (egg and fruit), (egg and cereal) } where a subset means all the element of A can be found in B.