Question

Suppose two balanced, six-sided dice are rolled once and that the 36 possible outcomes
are equally likely. Find the following probabilities:
a. The sum of the numbers on the two faces is even.
b. The numbers on the two faces differ by two or more.

please explain

Answer 1

Total number of outcomes = 36

a) P(getting an odd number on a dies) = 3/6 = 0.5

P(getting an even number on a die) = 3/6 = 0.5

Sum of the two faces is even when either both dice show even or both dice show odd

P(sum of the numbers on the two faces is even) = P(both dice show even or both dice show odd)

= 0.5x0.5 + 0.5x0.5

= 0.5

b) P(numbers on the two faces differ by two or more) = 1 - P(both numbers are the same) - P(the numbers differ by 1)

= 1 - 6/36 - 10/36

[(1,2), (2,1), (2,3), (3,2), (3,4), (4,3), (4,5), (5,4), (5,6), (6,5) are the 10 cases in which the numbers differ by 1]

= 1 - 16/36

= 20/36

= 5/9