You roll two fair dice, one green and one red.

(a) are the outcomes on the dice independent?

i. yes
ii. no
(b) find p(5 on green die and 3 on red die). (enter your answer as a fraction.)
(c) find p(3 on green die and 5 on red die). (enter your answer as a fraction.)
(d) find p((5 on green die and 3 on red die) or (3 on green die and 5 on red (enter your answer as a fraction.)

a) i. Yes

b)

c)

d)  

Step-by-step explanation:

a) If we roll two different dice , then the outcomes on the dice are independent of each other.

So , if we roll two fair dice, one green and one red. , then the outcomes on the dice are independent.

Therefore , correct answer is "Yes".

b) Total outcomes on each die = 6      (1,2,3,4,5,6)

If any two event E and F are independent , then P(E and F)= P(E) x P(F)

P(E or F)= P(E)+P()

Find P(5 on green die and 3 on red die) = P(5 on green die) x P(3 on red die)

So ,P(5 on green die and 3 on red die)

c) P(3 on green die and 5 on red die) = P(3 on green die) x P(5 on red die)

So ,P(3 on green die and 5 on red die)

d) P((5 on green die and 3 on red die) or (3 on green die and 5 on red die))

= P(3 on green die and 5 on red die) + P(5 on green die and 3 on red die) (∵ Both are mutually exclusive.)

∴ P((5 on green die and 3 on red die) or (3 on green die and 5 on red die))

the first option is the answer.