Chapter 15.2, Problem 18P

Are the following correct nomuniform sample spaces for a throw of two dice? If so, find the probabilities of the given sample points. If not show what is wrong. Suggestion: Copy sample space ( 2.4 ) and circle on it the regions corresponding to the points of the proposed nonuniform spaces.

(a) First die shows an even number. First die shows an odd number.

(b) Sum of two numbers on dice is even.

First die is even and second odd.

First die is odd and second even.

(c) First die shows a number $\le 3$.

At least one die shows a number $>3$.