When a die is rolled once, the probability of 1 showing up is 1/6 .
When a die is rolled 14 times, the probability of 1 showing up 6 times is a binomial probability.
Let x = number of times 1 shows up
P(x=6) = 14C6 (1/6)^6 (5/6)^(14-6)
= 14C6 (1/6)^6 (5/6)^8 = 0.014982
It is a certainty. If the die is rolled often enough, the probability that two consecutive rolls show a six is 1.
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%
2/9
50/50 50/50? This is equal to 1 which would imply the probability of flipping a head is certain. Obviously not correct as the probability of flipping a head in a fair dice is 1/2 or 0.5
Probability is 1/8 or 0.125 or 12.5% Explanation: A fair dice with six sides (numbers) has a probability of 1/2 of rolling an even number. Note: 1/2 = 3/6, where the dice has 3 even numbers out of six total sides. The probability of three same dice all roll an even number is the probability of one of these (1/2) to the power 3, or (1/2) * (1/2) * (1/2) which equals 1/8.
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
If the die is fair, the answer is 3003/32768 = 0.0624 or approx 1 in 16.
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 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%
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