Question

Two fair dices were rolled. 27. How many possible outcomes there will be, if the order of dices are considered? 28 How many possible outcomes there will be, if the sum of the dices are recorded? 29. What is the probability of getting a result with the sum exactly equals to 6? (Round to 4 decimal places, if needed 0 What is the probability of getting a result with the sum less than 6? (Round to 4 decimal places, if needed.)

Answer 1

27) Let X = face value of first die

Y = face value of second die.

There are 6 * 6 = 36 possible outcomes as follows:

Y|X	1	2	3	4	5	6
1	(1,1)	(2,1)	(3,1)	(4,1)	(5,1)	(6,1)
2	(1,2)	(2,2)	(3,2)	(4,2)	(5,2)	(6,2)
3	(1,3)	(2,3)	(3,3)	(4,3)	(5,3)	(6,3)
4	(1,4)	(2,4)	(3,4)	(4,4)	(5,4)	(6,4)
5	(1,5)	(2,5)	(3,5)	(4,5)	(5,5)	(6,5)
6	(1,6)	(2,6)	(3,6)	(4,6)	(5,6)	(6,6)

28) There are 11 possible outcomes of X + Y as 2, 3 , 4, 5, 6, 7, 8, 9, 10, 11, and 12

29) P( X + Y = 6) = 5/36 = 0.1389

Because total possible outcomes = 5 as {(1,5 ); ( 2, 4); ( 3, 3); (4, 2); (5,1)}

And total outcomes = 36

30) P( X + Y < 6) = P(X + Y = 2) + P(X + Y = 3) + P(X + Y = 4) + P(X + Y = 5)

= (1/36)+(2/36)+(3/36)+(4/36) = 10/36 = 2.2778