Question

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

(a) are the outcomes on the dice independent?

(b) find p(1 on green die and 2 on red die)

(c) find p(2 on green die and 1 on red die)

(d) find p[(1 on green die and 2 on red die) or (2 on green die and 1 on red die)]

Answer 1

(a) yes

(b) 1/36

(c) 1/36

(d) 1/18

Explanation:

(a) yes they are independent as the outcome of one does not affect the outcome of the other.

(b) As the dice are fair, each possible number (1 through 6) has the same probability of being rolled.

P(1 on green die) = 1/6

P(2 on red die) = 1/6

Therefore, P(1 on green die) AND P(2 on red die) = 1/6 × 1/6 = 1/36

(c) Again, as the dice are fair, each possible number (1 through 6) has the same probability of being rolled.

P(2 on green die) = 1/6

P(1 on red die) = 1/6

Therefore, P(2 on green die) AND P(1 on red die) = 1/6 × 1/6 = 1/36

(d) p[(1 on green die and 2 on red die) OR (2 on green die and 1 on red die)

= 1/36 + 1/36

= 2/36

= 1/18