finding Probability A specific kind of small airplane used for dusting crops has two identical engines functioning independently of each other, but can be flown with only one engine. The past records of this kind of engine indicate a 3% mid-air failure rate for each engine. One such plane crashed while dusting crops, and mid-air engine failure was suspected. What is the probability that such an airplane is likely to crash due to mid-air engine failure? The way to solve this problem is by using conditional probability. Say A is the probability of crashing, and F is the probability of engine failure. Let F1 the probability of getting failure (3%) and F2 the probability of getting failure also on other engine. What A should be? what is the best way to solve this problem? Thanks

This seems a rather i'll stated problem. If you interpret "such an airplane" as an airplane that crashed, then you are finding the probability that both engines failed given that it crashed. So, with your notation, you want $P(F_1\cap F_2 | A ) ={P(F_1\cap F_2\cap A)\over P(A) }$. You can simplify and calculate $P(F_1\cap F_2\cap A)=P(F_1\cap F_2 )=(.03)^2$. However, nothing in the problem allows you to calculate $P(A)$. You're at a dead end.

Perhaps, the problem meant for you to find the probability $P(F_1\cap F_2)$.