Monday, 31 July 2017

dice - A six-sided die is rolled five times. What is the probability that only the final roll will be a deuce?



A six-sided die is rolled five times. What is the probability that only the final roll will be a deuce?




I've tried to reason this out myself but I can only think that there's a 1/6 chance that the roll will be 2 and another 1/5 chance for it to be the last one. What am I missing here?



Thanks!


Answer



Allow me to quote your reasoning:




1/5 chance for it to be the last one





Here is what is wrong with your reasoning: it is not guaranteed that only one roll will be a deuce. It is also possible that there are two deuces rolled.






We need the first four rolls to be not deuce and the last one to be a deuce. Each roll is independent, so we can multiply the probabilities for each roll together.



The probability for a roll to be a deuce is 16, and similarly the probability for a roll to be not a deuce is 56. Therefore, the required probability is (56)4(16)=6257776.


No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find limh0sin(ha)h without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...