Question

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.

Answer 1

Explanation:

We are given that : For breakfast Bob has three options: cereal, eggs or fruit. He has to choose exactly two items out of the three available.

Part a ) Describe the sample of this experiment.

Since we have to choose two items out of the three available. So number of possible outcomes could be:

i) Cereal , Eggs

ii) Cereal , Fruit

iii) Eggs , Fruit

Thus sample space is S = { (Cereal , Eggs) , ( Cereal , Fruit ) , ( Eggs , Fruit ) }

Part b) A : Bob's breakfast includes cereal , we have to express this event as a subset of sample space.

Thus two outcomes includes Cereal = (Cereal , Eggs) , ( Cereal , Fruit )

Thus A = { (Cereal , Eggs) , ( Cereal , Fruit ) }