If the die is fair, the answer is 3003/32768 = 0.0624 or approx 1 in 16.
It is 0.0227
It is approx 0.1974
evens says 4 * 6 = 24 rolls required for 4 shows so 4 shows in 16 = 16 : 24 = 5 to 8 against
It is 0.2022
If both tosses are fair, the probability of that outcome is one in four.
The probability of getting three fives in the first three rolls and non-fives in the next three rolls is; P(5,5,5,N5,N5,N5) = 1/6 x 1/6 x 1/6 x 5/6 x 5/6 x 5/6 = 0.002679... The number of different order in which the fives can come out is given by; 6C3 = 6!/[3!∙(6-3)!] = 20 So the probability that in 6 rolls of a fair die exactly three fives (in any order) will come out is; P(three fives any order) = (20)∙(1/6)3∙(5/6)3 = 0.05358... ~ 5.4%
It is 0.0227
It is approx 0.1974
5 out of 36
evens says 4 * 6 = 24 rolls required for 4 shows so 4 shows in 16 = 16 : 24 = 5 to 8 against
It is 0.2022
If both tosses are fair, the probability of that outcome is one in four.
With a fair die, 1/6
It is a certainty. If the die is rolled often enough, the probability that two consecutive rolls show a six is 1.
The probability that a six will never show up in three rolls of a die is 125 in 216. The probability that a six will not show up in one roll is 5 in 6. Raise that to the third power to get 125 in 216.
2/9
The probability is 6/36 = 1/6.