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.)

it is probably the graph on the bottom right.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560