Answer to Question #173530 in Discrete Mathematics for ANJU JAYACHANDRAN

Question

4. a) A die is rolled twice and the sum of the numbers that appear is observed. What is

the probability that the sum is either a perfect square or a perfect cube?

Answer 1

perfect square is {4, 9}

perfect cube is {8}

All Events = {

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6),

}

4 can be obtained in 3 ways - Bold

9 can be obtained in 4 ways - Italics

8 can be obtained in 5 ways - Bold and Italics

So, answer = (3+4+5)/36 = 12/36 = 1/3

Answer: 1/3