1. An experiment consists of tossing a coin two times and observing the sequence of heads and tails.

(a) What is the sample space of this experiment?

(b) Describe the event "the first toss is a head" as a subset of the sample space?

2. A pair of four-sided dice-each with the numbers from 1 to 4 on their sides-are rolled, and the numbers facing down are observed. (Note: A four-sided die is similar to a pyramid with a triangular base.)

(a) List the sample space.

(b) Describe each of the following events as a subset of the sample space:

(i) Both numbers are even.

(ii) At least one number is odd.

(iii) Neither number is less than or equal to 2.

(iv) The sum of the numbers is 7.

(v) The sum of the numbers is greater than or equal to 6.

(vi) The numbers are the same.

(vii) A 2 or 3 occurs, but not both 2 and 3.

(viii) No 4 appears.