What are the odds of rolling a 4 3 times in a row?

Answer 1

You didn't say, but I'll assume you're rolling an honest pair of standard 6-sided dice.

The first cube can land in 6 different ways.
The second cube can land in 6 different ways.
The pair of them can land in (6 x 6) = 36 different ways.

Three of the possible rolls will show a 4 :

• 1 . . . 3
• 3 . . . 1
• 2 . . . 2

The probability of rolling a 4 on a single roll is 3 successes/36 possibilities = 1/12 .
The probability of rolling a 4 on the first roll is 1/12 .
The probability of rolling a 4 on the second roll is 1/12 .
The probability of rolling a 4 on the third roll is 1/12 .

The probability of rolling a 4 on all three rolls is (1/12 x 1/12 x1/12) = 1/1728 = 0.0005787 (rounded)
= 0.05787 percent.
If you're rolling a single cube, then you have 1 chance in 6 on each roll,
and the probability of three consecutive successes is
(1/6 x 1/6 x 1/6) = 1/216 = 0.00463 = 0.463 percent(rounded)