A die is loaded in such a way that an even number is twice as likely to occurs as an odd number. If E is the event that a number less than 4 occurs on a single toss of die, find P(E).

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:
E={1,2,3}
P(E)=1⁄9+2⁄9+1⁄9=4/9