2. Die Probability

You are rolling a die with 6 sides. Event $A$ is that you roll a number greater than 4. Event $B$ is that you roll a $1$. Event $C$ rolling a number less than 3. Answer these problems using python code. Make sure your numbers contain decimals (write 1.0 instead of 1) so python knows you want to have decimals. Each problem is worth 1 point.

What is the probability of event $A$?
If you roll once, what is the probability of rolling event $A$ or $C$?
If you roll event $B$, on your next roll what is the probability of event $A$?
What is the probability of rolling event $A$ followed by event $B$?
What is the probability of rolling event $A$ and event $B$ in the course of two rolls?
Why are your answers different for questions 2.4 and 2.5? Answer this in words using Markdown or Python.



In [6]:

    
#Answer 2.1
2 / 6









    Out[6]:





0.3333333333333333



In [7]:

    
#Answer 2.2
2/ 6 + 2 / 6









    Out[7]:





0.6666666666666666



In [8]:

    
#Answer 2.3
2 / 6









    Out[8]:





0.3333333333333333



In [9]:

    
#Answer 2.4
2 / 6 * 1 / 6









    Out[9]:





0.05555555555555555



In [10]:

    
#Answer 2.5
2 * 2 / 6 *  1 / 6









    Out[10]:





0.1111111111111111

Answer 2.6

2.5 Asks about a permutation and 2.6 about a combination.