Bayes Theorem probability Past Exam Paper Question -
Prof. Smith is crossing the Pacific Ocean on a plane, on her way to a conference.
The Captain has just announced that an unusual engine fault has been
signalled by the plane’s computer; this indicates a fault that only occurs once in
10,000 flights. If the fault report is true, then there’s a 70% chance the plane
will have to crash-land in the Ocean, which means certain death for the passengers.
However, the sensors are not completely reliable: there’s a 2% chance of
a false positive; and there’s a 1% chance of the same fault occurring without the
computer flagging the error report.
Question 
Formulate this problem in terms of conditional probabilities of outcomes, existence of
a fault and whether or not it is reported and use Bayes’ rule to compute Prof. Smith’s chances of survival. 
My Attempt
P(Fault) - 0.0001
P(Crash | Fault) - 0.7
P(FalsePositive | Fault) - 0.02
P(NoReport | Fault) - 0.01
I have no idea what to do next, every example I look at seems  a lot easier than this. Could someone help me out? 

Let $R=$"A fault is reported", $F=$"A fault occurs" and $C=$"The plane must crash-land". Then a false positive is $R\cap F^c$, a non-reported fault is $R^c\cap F$. We are given $P(F)=1/10000$, $P(C|F\cap R)=70/100$, $P(R\cap F^c)=2/100$ and $P(R^c\cap F)=1/100$. We want to calculate $P(C^c)=1-P(C)$. By Baye's rule, $P(C)=\frac{P(C|F\cap R)P(F\cap R)}{P(F\cap R|C)}$.But $P(F \cap R)=P(F)P(F|R)=98/1000000$, and $P(F \cap R|C)=98/100$. Hence $P(C^c)=1-(70.98.100)/(100.1000000.98)=1-7/100000$
