Possible outcomes of rolling a die 5 times = 6^5
Number of outcomes including rolling exactly one 4: 5^5 (5*5^4)
5^5/6^5 = 3125/7776 ~= 0.4019
When a number cube is rolled twice, there are 36 possible outcomes. (1,1),(1,2),....(6,6). (3,3) occurs only once. Therefore, the probability of rolling a 3 both times is 1/36.
1/12 possibilty.
The probability of rolling a six is one in six. The probability of rolling three consecutive sixes is one in 216. (1/6 x 1/6 x 1/6 = 1/216)
The probability is 0.2503
The probability of rolling at least one 2 when rolling a die 12 times is about 0.8878. Simply raise the probability of not rolling a 2 (5 in 6, or about 0.8333) to the 12th power, getting about 0.1122, and subtract from 1.
25/36
It is 0.8217
50% chance
The probability of rolling a 6 is 1/6. The probability of rolling 10 times a 6 is (1/6)10 or 1.654X10-8.
15
Possible outcomes of rolling a die 5 times = 6^5 Number of outcomes including rolling exactly one 2: 5^5 (5*5^4) 5^5/6^5 = 3125/7776 ~= 0.4019
The probability of a one being rolled in a fair die is 1 in 6, or 0.1666... . The probability of a one not being rolled is 5 in 6, or 0.8333... . The probability, then, of exactly one one being rolled in nine rolls is 1 in 6 times 5 in 6 to the 8th power, or about 0.0388.
The probability of rolling a 5, based on the information given, is 80/375 or 16/75. Your problem describes a relative frequency approximation of probability.
The probability of rolling a six is 1 out of 6, or 1/6. Now, perhaps your question is: If I roll a die 180 times, what is the probability of rolling a six at least once. This is the same as rolling a die 180 times and never once rolling a six. The probability is (5/6)180 which is 5.59 x 10-15.
It is 0.375 = 3/8
When a number cube is rolled twice, there are 36 possible outcomes. (1,1),(1,2),....(6,6). (3,3) occurs only once. Therefore, the probability of rolling a 3 both times is 1/36.
The probability that 14 is rolled at least once is 1 - 5.5*10-32 which, for all intents and purposes, can be treated as 1.