Probability airplane returns in 30 or 40 minutes given not back in 20

[lehaihua]

hi all,
I have a question that i really want to know the answer.

the probability that an airplane will return in 10min is 30%, in 20min is 30%, in 30min is 0%,
in 40min is 40% according to the past history records. given that the airplane has not return
in 20min, what is the probability that the airplane will return in 30 min and in 40 min?

i really stuck on this question since the formula doesn't seem to work[P(a|b) = P(a and b)/P(a)]

please give me some hint!thx thx

 

[olliemath]

Your formula should work perfectly well, you just need a little thought to work out what your a and b should be in this case.
What is the probability that the plane does not return in 20 minutes?
If it returns in e.g 30 minutes then clearly it doesn't return in 10 minutes, so P(30 mins and not 10 mins)=P(30 mins), what other simplifications can you make?