Prob(Rolling 2 when rolling 1200 times) = 1 - Prob(not rolling 2 when rolling 1200 times) = 1 - (5/6)1200 = 1 [accurate to 95 decimal places] That is, it is virtually a certainty.
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
Suppose A is the event {rolling a 6-sided die 20 times and getting a 5} Then A', the complement of A, is the event {rolling a 6-sided die 20 times and not getting a 5 any times} So Pr(A) = 1 - Pr(A') = 1 - (5/6)20 = 1 - 0.026084 = 0.973916 (to 6 dp)
3 out of 18
Prob(Rolling 2 when rolling 1200 times) = 1 - Prob(not rolling 2 when rolling 1200 times) = 1 - (5/6)1200 = 1 [accurate to 95 decimal places] That is, it is virtually a certainty.
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.
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
The probability of rolling a six on a die 6 times in a row is 1 in 46,656, or 0.000021433. The calculate that, the probability of rolling one 6 is 1 in 6. Simply raise that to the sixth power to get 1 in 46,656.
The probability of rolling a six with a standard die five times in a row is (1 in 6)5 which equals 1 in 7776 or about 0.0001286.
25/36
Suppose A is the event {rolling a 6-sided die 20 times and getting a 5} Then A', the complement of A, is the event {rolling a 6-sided die 20 times and not getting a 5 any times} So Pr(A) = 1 - Pr(A') = 1 - (5/6)20 = 1 - 0.026084 = 0.973916 (to 6 dp)
1 in 216
1 out of 100
3 out of 18
It is 1/216.