Question

You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? (b) Find P(6 on green die and 4 on red die). (c) Find P(4 on green die and 6 on red die). (d) Find P((6 on green die and 4 on red die) or (4 on green die and 6 on red die)).

Answer 1

Explanation:

d

Answer 2

A. The outcome on the dice are independent hence yes

B. P(6 on green die and 4 on red die) = 1 / 36

c. P(4 on green die and 6 on red die) = 1 / 36

d. P((6 on green die and 4 on red die) or (4 on green die and 6 on red die)) = 1 / 18

How to solve for the probability

b. P(6 on green die and 4 on red die)

This is a fair die. Each outcome on the die only has 1 / 6 probability

hence

P(6 on green die) = 1 / 6

P(4 on red die) = 1 / 6

P(6 on green die and 4 on red die) = 1 / 6 * 1 / 6 = 1/36

c. P(4 on green die and 6 on red die)

just as we have done above

each still has 1 / 6 probability of happening

= 1 / 6 * 1 / 6

= 1 / 36

d. P((6 on green die and 4 on red die) or (4 on green die and 6 on red die)).

This is P((6 on green die and 4 on red die) + (4 on green die and 6 on red die)).

P((6 on green die and 4 on red die) = 1 / 36

p(4 on green die and 6 on red die) = 1 / 36

= 1 / 36 + 1 / 36

= 2 / 36

= 1 / 18