Question: A two die, one is a fair dice and the other is an unfair dice.

Please show all steps and explanations! I want to learn the process behind it!

Fair dice

x	p(x)
1	1/6
2	1/6
3	1/6
4	1/6
5	1/6
6	1/6

Unfair dice

x	p(x)
1	1/12
2	2/6
3	1/12
4	2/6
5	1/12
6	1/12

Events:

E1: Rolling at least one 4

E2: Rolling a total of 12

Calculate

P(E1)

P(E2)

P(E1 AND E2)

P(E1 OR E2)

P(E1 | E2)

P(E2 | E1)