The probability of rolling a total of 7 on the two dice is 8/63 if in the particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio 1:2:3:4:5:6.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Ratios are 1:2:3:4:5:6

Then,

x + 2x + 3x + 4x +5x + 6x = 1

21x = 1

x = 1/21

The possible combinations of two rolls that total 7 are:

The probability P of rolling a total of $7$ on the two dice is equal to the sum of the probabilities of rolling each combination.

[tex]\rm P = \dfrac{1}{21}\cdot\dfrac{6}{21}+\dfrac{2}{21}\cdot\dfrac{5}{21}+\dfrac{3}{21}\cdot\dfrac{4}{21}+\dfrac{4}{21}\cdot\dfrac{3}{21}+\dfrac{5}{21}\cdot\dfrac{2}{21}+\dfrac{6}{21}\cdot\dfrac{1}{21}\\\\=\dfrac{8}{63}[/tex]

Thus, the probability of rolling a total of 7 on the two dice is 8/63 if in the particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio 1:2:3:4:5:6.

Learn more about the probability here:

brainly.com/question/11234923

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