For a particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio $1:2:3:4:5:6$. What is the probability of rolling a total of 7 on the two dice

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.

What is probability?

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.

Let x be the probability of rolling a 1.

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:

{(1,6) ; (2,5) ; (3,4) ; (4,3) ; (5,2) ; (6,1)}

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.

7on the two dice is8/63if in theparticular peculiar pairofdice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio 1:2:3:4:5:6.## What is probability?

ratioof thenumberoffavourableoutcomes to thetotal numberofoutcomes, in other words, theprobabilityis thenumberthat shows thehappeningof theevent.Let x be the probability of rolling a 1.{(1,6) ; (2,5) ; (3,4) ; (4,3) ; (5,2) ; (6,1)}7on the two dice is8/63if in theparticular peculiar pairofdice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio 1:2:3:4:5:6.probabilityhere:Step-by-step explanation: