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

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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).

الأجوبة

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

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أسئلة مشابهة

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).
Fair die loaded in way even number appear is twice likely than odd number. Find probability appear prime number if die tossed once.
Tossing a die one time, let A be the event that an odd number occurs, B that a prime number occurs
Tossing a die one time, let A be the event that an even number occurs, B that a prime number occurs

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