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? 

When confused, it is useful to break the problem into parts, and work through a fictitious scenario.
The prof will survive all false alarms and $30\%$ of correct alarms
Suppose the prof takes $1,000,000$ trips (to avoid decimals)
A fault is likely to occur $100$ times, of which $99\% \;\; or\;\;99$ would sound the alarm,
and not occur $999,900$ times, of which $2\%\;\; or\;\; 19,998\;$ would sound false alarms
Thus of the $99+19,998 = 20097$ times the alarm sounds,
the prof will survive in $19,998+ 30\%$ of $99 = 20027.7$ times 
and P(prof survives) $=  \dfrac{20027.7}{20097} = 99.6551724..\%$
Added
Once you have got the scenario clearly mapped out, you should easily be able to put it in the usual mould for Bayes' rule. The important thing is to first get it clearly into your head.
PS:
To match with terminology in main answer,
P(Correct alarm)  =P(fault)*P(alarm|fault) = $\dfrac1{10,000}\times(1-0.01) = \dfrac{99}{1,000,000}$
P(False alarm)  = P(no fault)*P(alarm|no fault) $= \dfrac{9999}{10,000}\times(0.02) = \dfrac{19,998}{1,000,000}$
P(survive|alarm) $$= \dfrac{\text{P(survive|false alarm)*P(false alarm) + P(survive|correct alarm)*P(correct alarm)}}{\text{P(false alarm) + P(correct alarm)}}$$ 
Cancelling out the denominators, $$P(survive|alarm) =\dfrac{1*19,998+0.3*99}{19,998+99}= 99.6551724..\%$$
