An experiment consists of throwing two dice.
(a) Write down the sample space of this experiment
(b) If E is the event "total score is at most 10", list the outcomes belonging to $E^c$.
(c) Find the probability that the total score is at most 10 when the two dice are thrown.
(d) What is the probability that a double will not be thrown.
(e) What is the probability that a double is not thrown nor is the score greater than 10?
My Work:
(a) S={{1,1},{1,2},…{6,6}}
(b) $E^c$={{5,6},{6,5},{6,6}}
(c ) P(Score at most 10)=1-P(greater than 10)=$1-\frac{3}{36}=\frac{11}{12}$
(d) P(No double thrown)=1-P(Double Thrown)= $1-\frac{6}{36}=\frac{30}{36}=\frac{5}{6}$
(e) I'm not sure how to solve this part. Just looking at the sample space I know it should be $\frac{28}{36}$ but I want to know how to solve this mathematically.
Any help is appreciated.
Best Answer
(e) Is $1$-P(Double Thrown)-P(Greater than 10)+P(Double Thrown and Greater than 10) $$1-\frac{6}{36}-\frac{3}{36}+\frac{1}{36}$$
One must add back in the final part to avoid double counting the $\{6,6\}$