A red and a blue die are thrown. Both dice are loaded (that is, not all sides are equally likely).

A red and a blue die are thrown. Both dice are loaded (that is, not all sides are equally likely). Rolling a 2 with the red die is twice as likely as rolling each of the other five numbers and rolling a 4 with the blue die is twice as likely as rolling each of the other five numbers.

a. What is the probability of each outcome of the red die?

b. What is the probability of each outcome of the blue die?

c. What is the probability that the sum of the numbers on the two dice is 6?

My attempt

a. Red die probability

1- 1/7

2- 2/7

3- 1/7

4- 1/7

5-1/7

6- 1/7

b. Blue die probability

1 - 1/7

2 - 1/7

3 - 1/7

4 - 2/7

5 - 1/7

6 - 1/7

c) Sum of nos. as 6 for both die

Various possible combinnations (Red, Blue) with probabilities as below

(1,5) - (1/7(1/7)

(2,4) - (2/7)(2/7)

(3,3) - (1/7)(1/7)

(4,2) - (1/7)(1/7)

(5,1) - (1/7)(1/7)

Overall probability - 4. (1/7)2 + (2/7)2 = 16.32%