1.state the Axioms of property
2.suppose that A and D are independent event such that the
probability that neither occurs is a and the probability of B
occuring is b. show that p(A)=1-b-a/1-b
3.A die is weighted so that 4 is twice as likely to appear as the
number 1,2,3,5 and 6 is twice as likely to appearas 4
find the probability of obtaining an even number of a single row on the die

Well it can be written simply as A+B+a+b=1

where A=probability of A
B=prob of B
a=neither
and b=both

the both can be written also as the probability of A x prob of b

ie. b=AB

therefore
A+B+a+AB=1
A(1+B)=1-B-a
A=(1-B-a)/(1+B) which is almost what you had in the question but i think this should be the answer

3. The probability of the dice can be written as follows;
1=x
2=x
3=x
4=2x
5=x
6=4x

therefore
10x=1
x=0.1
and therefore as the even numbers add up to 7x the prob is 0.7

Hope that helps
Chris