Since there are 6 numbers (1-6) on each die, and you're rolling it 5 times, the total number of possibilities is 65. You now have to find out, out of the total, how many possibilities fill your requirements. For 5 rolls of one the chance is 1/65. There are 5 possible sets of rolls where you'll get 4 1s (4 1s and a 2, 3, 4, 5, or 6). Lastly there are 25 possible sets of rolls where you'll get 3 1s (3 1s and a 2 and 2 or a 2 and 3 or a 2 and 4 etc). so adding up all the possibilities that is 31/65. That is a percentage of .4% or 4 out of 1000 rolls of all the dice you will get 3, 4, or 5 1s. Sounds like a yahtzee question.
5 out of 36
7/8
One way of describing a fair trial in statistics is one in which the probability of each outcome is what might be expected on theoretical grounds. A coin, that can only land on two faces, is equally likely to land on either one. A cubic die that is equally likely to show any one of its six faces and so on.
6 outcomes for each die and so 6x6x6 outcomes for all three
1/2 * 1/2 * 1/2 = 1/8 = 12.5%
It is approx 0.1974
With a fair die, it is 1/216 in three rolls, but the probability increases to 1 (a certainty) as the number of rolls is increased.
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%
As soon as the ball touches first base, it is a fair ball, regardless of what happens after that.
Yes, it would be fair as long as it is fielded before first or third base or comes in contact with the base.
Rolling a sum of 15 on three rolls of a die, when the first roll is a 4, is the same as rolling a sum of 11 on the second and third roll. The probability of rolling 11 on two dice is 3 in 36, or 1 in 12.
It is 0.0227
It would be considered a fair ball.
1 in 36.
If the die is fair, the answer is 3003/32768 = 0.0624 or approx 1 in 16.
the three fifths compromise was not fair
Yes, the entire line is in fair territory.