SOLUTION: If b and w stand for the results of a throw of two dice, show that the events A = {b +w < 8} and B = {b = 3 or 4} are statistically independent (although it is difficult to see w

Algebra ->  Probability-and-statistics -> SOLUTION: If b and w stand for the results of a throw of two dice, show that the events A = {b +w < 8} and B = {b = 3 or 4} are statistically independent (although it is difficult to see w      Log On


   

Question 586525: If b and w stand for the results of a throw of two dice, show that
the events A = {b +w < 8} and B = {b = 3 or 4} are statistically independent
(although it is difficult to see why they should be in the usual sense of the word)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If b and w stand for the results of a throw of two dice, show that
the events A = {b +w < 8} and B = {b = 3 or 4} are statistically independent
----
P(A) = 5/36
P(B) = 2/6 = 1/3
---
P(A)*P(B) = (5/36)(1/3) = 5/108
-----
P(A | B) = ?
If b = 3 then w is 5 or4 or 3 or 2 or 1
If b = 4 then w is 3 or 2 or 1
-
So P(A | B) = 8/36
-----
Since 5/108 # 8/36, A and B are independent.
==============================================
Cheers,
Stan H.