It is 0.2022
It is 0.0227
It is approx 0.1974
When a die is rolled once, the probability of a 4 showing up is 1/6. Apply the binomial probability for finding the probability of exactly three fours out of 12 throws of a die. n=12 (number of throws) p=1/6 (probability of a four in a single throw) x = 3 (number of times out of 12 , a four showing up) P(x=3) = 12C3 (1/6)^3 (5/6)^(12-3) = 12C3 (1/6)^3 (5/6)^9 = 0.197443
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.
If the die is fair, the answer is 3003/32768 = 0.0624 or approx 1 in 16.
5 out of 36
It is a certainty. If the die is rolled often enough, the probability that two consecutive rolls show a six is 1.
It is 0.0227
It is approx 0.1974
When a die is rolled once, the probability of a 4 showing up is 1/6. Apply the binomial probability for finding the probability of exactly three fours out of 12 throws of a die. n=12 (number of throws) p=1/6 (probability of a four in a single throw) x = 3 (number of times out of 12 , a four showing up) P(x=3) = 12C3 (1/6)^3 (5/6)^(12-3) = 12C3 (1/6)^3 (5/6)^9 = 0.197443
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.
If the die is fair, the answer is 3003/32768 = 0.0624 or approx 1 in 16.
If both tosses are fair, the probability of that outcome is one in four.
evens says 4 * 6 = 24 rolls required for 4 shows so 4 shows in 16 = 16 : 24 = 5 to 8 against
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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%
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 . . . 33 . . . 12 . . . 2The 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)