Question

In an experiment, two fair dice are tossed and at the same time,two fair coins are thrown. Find the probability of obtaining a total score of 7 on the dice and two heads on the coins

Answer 1

Surprisingly, it doesn’t matter if the two dice have the same number of sides. The probability is 1/N, where N is the number of sides on whichever die has the greater number of sides. The number of sides on the die with fewer sides does not affect to the result.

So rolling a pair of fair and identical six-sided dice, the odds they will show the same number is 1 in 6.

Rolling a eight-sided die along with a twenty-sided die, the odds they show the same number is simply 1 in 20.

Note: When asking questions regarding dice, one needs to remember that a wide variety of dice types with different shapes, numbers of sides, and numbering schemes have been mass produced. One can not simply take for granted that a fair dice necessarily means a six-sided cube. If we include doubling die (such as used in backgammon), or ten-sided percentile dice (where one die of the pair is numbered 00, 10, 20, 30, etc.) then the formula above might not apply.