Answer:
(1.37) AUB = { 1,2,3,4,5,6}
(1.38) AUC = { 1,2,3,4,5 }
(1.39)BUC = { 1,2,3,4,5,6}
(1.40) { 2,4 }
(1.41) { 1,3,5 }
(1.42) { phi }
(1.43) AU(BUC) = { 1,2,3,4,5,6 }
(1.44) { phi }
(1.45) {1,2,3,4,5}
(1.46) { 1,2,3,4,5 }

2 / 4 x 100
= .50 x 100
= 50%
By the chain rule,

where
.
We have component partial derivatives






Putting the appropriate pieces together and setting
, we get


The US Senate is composed of 2 Senators from each of the 50 states to give a total of 100 people in the Senate.
4+2+8+6 = 20 total
8 purple
so 8/20 reduced to 2/5 chance for a purple
then there will be 19 left
6 blue =
6/19 probability of having a blue one
2/5 * 6/16 = 12/80 reduces to 3/20 probability total