A die is loaded in such a way that an even number is twice as likely to occurs as an odd number

The sample space is:
S={1,2,3,4,5,6}
We assign a probability of w teach odd number and a probability of 2w to each even number. Since the sum of probabilities must be 1, we have:
9w=1 or w=1⁄9
Hence probabilities of 1⁄9 and 2⁄9  are assigned to each odd and even number respectively, therefore:
A={2,4,6}    ,   B={3,6}
A∪B={2,3,4,6}       ,A∩B={6}  
P(A∪B)=2⁄9+1⁄9+2⁄9+2⁄9=7/9
P(A∩B)=2/9