Question

a six sided die is rolled 4 times in a row. What is the probability of getting 4 only on the last trial of this experiment?

Answer 1

First, start of by saying what the probability of getting a 4 is, which is 1/6.
Now, this means the probability of not getting a 4 is 1-(1/6)=(5/6), since the total probability is 1.

After doing this, you should think about what it means to only get 4 on the last trial, the 4th trial.  It means that the probabilities of the 1st, 2nd, and 3rd trial were (5/6) each.  The 4th trial had a probability of (1/6).  So the probability would be calculated as following: ($(5/6)^3*(1/6)$=$5^3/6^4$.  You can use a calculator or your computer to find out that the probability is 125/1296.  

I hope this was helpful!