Question

If two fair dice are rolled, what is the probability that the total showing is either even or less than nine?A. 5/6B. 29/36C. 3/4D. 8/9

Answer 1

Above we can find all the 36 possible outcomes of rolling two dices:

(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)

Now, the outcomes that match the total showing is either even or less than nine:

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

Then, 30 out of 36 outcomes are desired. Therefore, the probability is:

`P=(30)/(36)=(5)/(6)`

ANSWER

A. 5/6