5 5 pts Two fair dice are tossed and the up face on each die

5. (5 pts) Two fair dice are tossed, and the up face on each die is recorded. (a) (2 pts) List the 36 simple outcomes contained in the sample space.

The 36 possible outcomes are (13 means 1 in first die and 3 in second die, not thirteen):

11,12,13,14,15,16,21,22,23,24,25,26,31,32,33,34,35,36,41,42,43,44,45,46,51,52,53,54,55,56,61,62,63,64,65,66

P[The sum of the numbers is 10] = 3/36 =1/12 (favourable cases being 46,55,64)

P[The sum of the numbers is even] = P[either both the numbers are even or both are odd]

=P[Both are even] + P[Both are odd]

= 9/36 + 9/36 =1/4+1/4=1/2

P[5 appears on at least one of the dice] = 11/36