Stat 200 Chapter4: Problem 1

Two fair dice, one blue and one red, are tossed, and the up face on each die is recorded. Define the following events:

E:E: {{ The numbers are equal }}

F:F: {{ The difference of the numbers is 3 or more }}

Find the following probabilities:

P(E)=P(E)=
16​

P(F)=P(F)=
12​

P(EandF)=P(EandF)=
112​

P(E|F)=P(E|F)=

P(F|E)=P(F|E)=

Are events E and F independent?