Standard 6 sided die is weighted so that the probabilities of rolling 2,3,4,5 or 6 are equal and the probability of rolling 1 is three times the probability of rolling a 2. if the die is thrown twice, what is the probability that the sum of the numbers thrown will be 4

There are 6 sides of the die, let us say that side 1 is S1, side 2 is S2 and so on.

Assigning a value of 3 to S1, so the probabilities are:

Probability

S1 = 3 3/8

S2 = 1 1/8

S3 = 1 1/8

S4 = 1 1/8

S5 = 1 1/8

S6 = 1 1/8

total = 8

The combinations that the sum of the two rolls will be 4 are:

S1 and S3

S3 and S1

S2 and S2

So the total probability is:

P = (3/8) * (1/8) + (1/8) * (3/8) + (1/8) * (1/8)

P = 0.1094 = 10.94%

So there is about 0.1094 or 10.94% probability that the sum will be 4.