Question 665417: 1. Assume you roll two fair dice. Let A be that the sum of the two dice is even. Let B be that the sum of the two dice is six or below.
a.) what is P(A u B)?
b.) what is P(A n B)
2.P(AIB) = .6 and P(A) = .6. what can we say about A and B?
I literally read the chapter three times and, for the life of me, cannot figure out these questions!
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Two dice are rolled
( 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
Let A be the event that the sum on the top face be even
A={( 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 )}
n(A)= 18
p(A)= 18/36= 1/2
B is the eventy that the sum on upper face is 6 or less than 6
B={( 1 , 1 ), ( 1 , 2 ) ( 1 , 3 ) ( 1 , 4 ) ( 1 , 5 ) ( 1 , 6 )
( 2 , 1 ) ( 2 , 2 ) ( 2 , 3 ) ( 2 , 4 ) ( 3 , 1 ) ( 3 , 2 ) ( 3 , 3 )
( 4 , 1 ) ( 4 , 2 ) ( 5 , 1 ) }
n(B)=16
p(B)= 16/36 = 4/9
(A n B) =( 1 , 1 ), ( 1 , 3 )( 1 , 5 )( 2 , 2 ) ( 2 , 4 )( 3 , 1 )( 3 , 3 )( 4 , 2 ) ( 5 , 1 )}
n(AnB)= 9
p(AnB)= 9/36 = 1/4
p(A u B) = p(A)+p(B) -p(a n B)
= 1/2 +4/9 -1/4
=(18+16-9)/36
=23/36
P(AIB) = .6
or, P(A and B)/P(B) = 0.6
or, P(A)*P(B)/P(B) = 0.6
or, P(A) = 0.6
So, A and B are independent.
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