Suppose die is weighted such that the probability of rolling a three is the same as rolling a six, the probability of rolling a one, two, or four is 3 times that of a six, and the probability of rolling a five is 4 times that of rolling a three. Find the probability ofRolling a onerolling a tworolling a threerolling a four

Question
Asked Sep 12, 2019

Suppose die is weighted such that the probability of rolling a three is the same as rolling a six, the probability of rolling a one, two, or four is 3 times that of a six, and the probability of rolling a five is 4 times that of rolling a three. Find the probability of

Rolling a one

rolling a two

rolling a three

rolling a four

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Expert Answer

Step 1

Suppose die is weighted such that the probability of rolling a three is the same as rolling a six, the probability of rolling a one, two, or four is 3 times that of a six, and the probability of rolling a five is 4 times that of rolling a three. Then

P(3) P(6)
P(1) P(2)P(4) 3P(6)
P(5) 4P(3)
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P(3) P(6) P(1) P(2)P(4) 3P(6) P(5) 4P(3)

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Step 2

The total probability of the events of rolling one, rolling2, ...

Р(1)+ P(2)+ P(3)+ P(4)+P(5)+P(6)-1
ЗР(3) + ЗР (3)+ Р(3)+ ЗР(3)+4P(3)+ P(3) -1
15P(3)1
1
Р(3) -3;
15
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Р(1)+ P(2)+ P(3)+ P(4)+P(5)+P(6)-1 ЗР(3) + ЗР (3)+ Р(3)+ ЗР(3)+4P(3)+ P(3) -1 15P(3)1 1 Р(3) -3; 15

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