急！！probability question

a)P(yellow AND it is in U)=2/6=1/3
P(yellow AND it is in V)=1/6
P(yellow)=P(V)+P(U)
=(1/6+1/3)/2=1/2 =0.5

b)P(yellow AND it is in U)/P(yellow)
=(1/3)/(1/2)=2/3

C)THERE are 9 kinds of method to be chosen
1.yellow(ball A) in U AND blue ball in U
2.yellow(ball B) in U AND blue ball in U
3..yellow(ball A) in U AND blue (ball A) in V
4...yellow(ball A) in U AND blue (ball B) in V
5.yellow(ball B) in U AND blue (ball A) in V
6.yellow(ball B) in U AND blue (ball B) in V
7.yellow ball in V AND blue ball in U
8.yellow ball in V AND blue(ballA) in V
9.yellow ball in V AND blue(ballB) in V

however,there are just(1)and(2)are selected urn is U...SO the probability is 2/9

d)THE probability that the urn selected are both are yellow and they are in U:
P(both are yellow and they are in U):2/6X2/6=4/36=1/9
P(both are yellow and they are in V):1/6X1/6=1/36
the P(both are yellow)=1/9+1/36 =5/36
GIVEN that both are yellow...FIND it selected is U
P(both are yellow and they are in U)/P(both are yellow)
=(1/9)/(5/36)
=4/5

a) 1/2 x (2/3) + 1/2 x (1/3)
=2/6 + 1/6
=1/2 //

b) P( Y from U ) : P( Y from V)
= 2/3 : 1/3
=2:1
the probability that selected urn is U is 2/(2+1) = 2/3 //

c) P(1st ball yellow & 2 nd ball from U : P(1st ball yellow & 2nd blue from V)
= 2/3 x 1/3 ; 1/3 X 2/3
=2/9 : 2/9
=1:1
the probability that the urn selected is U =1/(1+1) = 1/2 //

d) P( both yellow from U) : P( both yellow from V)
=2/3 X 2/3 : 1/3 X 1/3
=4/9 : 1/9
=4:1
the probability that urn selected is U = 4/(4+1) = 4/5 //

2007-11-20 23:32:51 補充：
c) P(1st ball yellow & 2 nd ball from U ): P(1st ball yellow & 2nd blue from V)= 2/3 x 1/3 : 1/3 X 2/3=2/9 : 2/9=1:1 the probability that the urn selected is U =1/(1┼ 1) = 1/2 //