Maths Question- An aircraft is designed to operate with 99.99% reliability over 100hrs of flight.?

i'm not sure if correct way, i'll give shot.

consider problem in terms of binomial distribution, because each block of 100 hours of flight can considered independent events (i.e. not conditional probability).
pr(success)= 0.9999
pr(failure )=0.0001
number of trials=x
number of successes=x

therefore;

ncr(x,x) * [pr(success)]^(x-0) * [pr(failure)]^(x-x)=0.5
[pr(success)]^x=0.5
0.9999^x=0.5
x= 6931.1252 (to 4 decimal places)

means 6931.1252 sets of 100 hour blocks, translating approximately 693113 hours.

way think of visualize tree diagram. have 2 branches, split off further 2 branches, etc... if top branch represents probability of success (i.e. probability 0.9999) , bottom branch represents failure, how many times have go along top branch before reach probability of 0.5 (i.e. 0.9999^x=0.5, solve x)? remember when go along branch, multiply, , when go across branches add.

way, in case it's not clear, ncr(n,m) means 'n choose m', or number of ways 'n' objects can chosen total of 'm' objects.

here's question- how long aircraft need operate chance of continuous successful operation reduce 50%? i'm more interested how problem solved, not answer.

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