A die is loaded in such a way that an even number is twice as likely to occurs as an odd number. If A is the event that an even number turns up and let B the event that a number divisible by 3 occurs, find P(A∪B) and P(A∩B).

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

The sample space is:

need an explanation for this answer? contact us directly to get an explanation for this answerS={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