Here is the solution to the following similar problem:

Fill in the missing probabilities, given that the outcome 6 is three times as likely as the outcome 1:

Outcome 123 456
Probability       .125 .125 .125 .125      

Solution Let us take P(1) to be x. Then we get the following table:

Outcome 123 456
Probability  x   .125 .125 .125 .125  3x 

(since P(6) is 3 times P(1)).

Since the probabilities must add to 1, we now get

or

Solving for x, we get x = .125, and so 3x = .375, allowing us to fill in the table as follows:

Outcome123 456
Probability .125 .125 .125 .125 .125  .375 

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