The probability of (1 or 2 or 3) on the first (or any) roll is 1/2 = 50% .
The probability of (4 or 5 or 6) on the second (or any) roll is 1/2 = 50% .
The probability of exactly that result on two rolls is (1/2 x 1/2)= (50% x 50%) = 1/4 = 25% .
1/6,3/6 ----------------------------------------------------------------------------------------------------- The probability of rolling a 2 is: P(2) = 1/6 The probability of rolling an even number is: P(even) = 1/2 The result on the second roll is independent of the result in the first roll. The probability of rolling a 2 and then rolling an even number is: P(2,even no.) = (1/6) ∙ (1/2) = 1/12 = 0.08333... ≈ 8.33%
Assuming that a dice roll is purely random, there is a 1 in 6 probability of landing on any number. Since the second roll depends on the probability of the first, they factor together: First Roll: 1/6 Second Roll: (1/6)(1/6) = 1/36 If you were rolling both dice at once, however, the math would be completely different.
The first roll doesn't matter for probability, it just sets the number to be rolled by the other two. So: P(rolling the same number three times) = P(rolling a particular number)2 = (1/6)2 = 1/36
The first number doesn't matter, just that the last three are the same as the first. P(rolling the same as the number before) = 1/6 P(rolling the same number as the first three times = (1/6)3 = 1/216
The probability of rolling a sum of 8 on one roll of a pair of dice is 5/36.The probability of not rolling a sum of 8 on one roll of a pair of dice is 31/36.The probability of rolling a sum of 8 twice on two rolls of a pair of dice is(5/36)(5/36) = (5/36)2 .The probability of rolling first a sum of 8 and then rolling a sum that is not 8 on thesecond roll is (5/36)(31/36).The probability of rolling a sum that is not 8 on the first roll and rolling a sum of 8in the second roll is (31/36)(5/36).So The probability of rolling a sum of 8 at least one of two rolls of a pair of dice is(5/36)2 + (5/36)(31/38) + (31/36)(5/36) = 0.258487654... ≈ 25.8%.
What is the probability of rolling a 6 the first time and a 1 the second time
None, because you cannot have the first or second dice: it is the first die or second die. The probability is 1/6 * 1/2 = 1/12
It is 1/2*1/3 = 1/6
The probability of rolling a 2 on the first roll is 1 in 6. The probability of rolling a 3 on the second roll is 1 in 6. However, the probability of rolling a 2 on the first roll and 3 on the second roll before you roll at all is 1/6 x 1/6 = 1 in 36.
1/6,3/6 ----------------------------------------------------------------------------------------------------- The probability of rolling a 2 is: P(2) = 1/6 The probability of rolling an even number is: P(even) = 1/2 The result on the second roll is independent of the result in the first roll. The probability of rolling a 2 and then rolling an even number is: P(2,even no.) = (1/6) ∙ (1/2) = 1/12 = 0.08333... ≈ 8.33%
First you need to work out the probability of rolling a prime number. The prime numbers on a die are 2, 3 and 5. Thus the probability of rolling a prime number is 3/6 which can be simplified to 1/2. The probability of rolling a number greater than 1 is 5/6. The probability of rolling one on one dice and one on the other is therefore 1/2 x 5/6 = 5/12. There are two possible ways round these options could come though. You might get the number greater than one on the first roll, and the prime on the second. Thus we need to multiply the probability by 2, which gives us the final answer of 5/6.
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The probability of throwing just one one with two dice can be calculated by considering the different ways it can occur. There are two ways to get one one: rolling a one on the first die and any number on the second die, or rolling any number on the first die and a one on the second die. There are a total of 36 possible outcomes when rolling two dice, so the probability is 2/36, which simplifies to 1/18.
(1/2) * (1/6) = 1/12
The probability that, when rolling three dice none will come up odd is broken down by the probability that on odd roll will occur as an independent event. Rolling the first die has a probability of 3/6 that it will be odd. Rolling the second has the probability of 3/6 that it will be odd. Rolling the third has a probability of 3/6 will be odd. Rolling three and coming up with odd is really the probability that no odd numbers occurred, so therefore an even number DID happen (3/6), and an even number DID happen (3/6), and an even number DID happen (3/6). That's really just 1 - (3/6^3) or simplified 1 - (1/2^3). So therefore the probability that an odd number occurred in 3 die rolls is about 87.5%.
1/6 on the first roll, and 1/6 of rolling a six on the second roll. Overall, the chances of you rolling a 5 on the first and a six on the second is 1/3.
The probability when you roll two dice that you roll an odd number on the first die and a 1 on the second die is 1 in 12. The two die are sequentially unrelated, so you can consider them separately. The probability of rolling an odd number is 3 in 6, or 1 in 2. The probability of rolling a 1 is 1 in 6. Multiply the two probabilities together and you get 3 in 36, or 1 in 12.