Rolling Dices and Chances

Question

Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 2; C: at least one of the numbers is 5; and D: the numbers do not add to 10. If the numbers do not add to 2, then how many elements does it contain.

Answer 1

Pr(R=4) = 1/6 = about 16.7%

Pr(2) = Pr(R=1 and G=1) = 1/6 x 1/6 = 1/36 = about 2.8%

Pr(at least one 5) = 1/6 + 1/6 = 2/6 = 1/3 about 33.3%

= Pr(R5) +Pr(G5)

Pr(~10) = 1-Pr(10) =1- 3/36 = 33/36 = 11/12= about 91.7%

there are 3 ways to get 10, two 5's, 6 & 4 or 4 & 6.

and 36 possible outcomes. divide 3 by 36

then subtract that from 1