2. In a board game, you must roll two 6-sided number cubes. You can only start the game
if you roll a 6 on at least one of the number cubes. NOTE: This is using two cubes.

a. Make a list of all the different possible outcomes when two number cubes are
rolled (Sample Space) (2 points possible)
b. What fraction of the possible outcomes is favorable, or in other words, what is the
theoretical probability of rolling a 6 on at least one number cube when rolling
the two number cubes? (3 points possible) Hint: Highlight each pair in the
sample space that had at least one 6 in the outcome to help you identify
"favorable events

A) Sample Space

(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)

B)Probability of rolling a 6

10/36

Step-by-step explanation:

A.         1         2        3         4       5         6

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

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

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

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

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

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

B.  11/36 or 0.3055555

Step-by-step explanation:

1. You can see there are 36 outcomes when rolling the dice.

2. Then you find that there are 11 possible outcomes with at least one 6. (For example 1-6 2-6 3-6.)

3. The chance of rolling at least one 6 in a pair of dice is 11/36.

4. 11 divided by 36 is 0.3055555.

(Though the calculator on Google says 0.305555556.)

step-by-step explanation:

let pq = qr = rs = x, and xz = y and zu = z.

if the horizontal lines are parallel, then corresponding segments are in proportion:

substitute:

therefore 3 = y = z.

xu = y + z → xu = 3 + 3 = 6