Question

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 sum of the numbers is even }}

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

Find the following probabilities:


P(E)=

P(F)=

P(EandF)=

P(E|F)=

P(F|E)=

Answer 1

Two fair dice are rolled so sample space is

S={(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)}

n(S) = 36

Now E is the event that the sum of the numbers is even

So

E= {(1, 1) (1, 3) (1, 5) (2, 2) (2, 4) (2, 6) (3, 1) (3, 3) (3, 5) (4, 2) (4, 4) (4, 6) (5, 1) (5, 3) (5, 5) (6, 2) (6, 4) (6,6)}

So n(E) = 18

Now F is the event that the difference of the numbers is 3 or more

So

F= {(1, 4) (1, 5) (1, 6) (2, 5) (2, 6) (3, 6) (4, 1)  (5, 1) (5, 2)  (6, 1) (6, 2) (6, 3) }

So n(F) = 12

For P(EandF) we will consider intersection of E and F

{(1, 5) (2, 6) (5, 1) (6, 2) }

So

Now

and

Please give thumbs up if you like the answer.