00:02
In a certain four -engine vintage aircraft, now quite unreliable, each engine has 15 % chance of failure on any flight, as long as it is carrying one -fourth share of the load, right? so we are talking about one engine, okay, out of four, remember.
00:28
So this is 15 % chance of failure which is given to us.
00:32
That is for a single engine okay remember this now it is said after this but if one engine fails then the chance of failure increases to 35 % for each of the other three engines right and if a second engine fails, each of the remaining two has 45 % chance of failure, right? assuming that no two engines ever fail simultaneously and the aircraft can continue flying with as few as two operating engines, right? find the probability of exactly one engine failure.
01:34
So remember, it is already given that there should be exactly one engine failure that's it right so background of this problem will be created from here only right we want to find out probability this is the key concept right just keep in mind what you have to find according to that you just need to take some thing or you can say grasp few values or you can say a few things of the extract you you can say extract a few values from here in the problem so that you can find out your answer.
02:17
Right.
02:18
So here we need to find the probability of exactly one engine failure.
02:30
Right.
02:31
So we need to find this.
02:34
Remember.
02:36
Right.
02:36
Only one.
02:37
Right.
02:38
So now what you can write here is first of all we are given with probability.
02:55
Of chance of failure of one engine out of four will be equal to this will be equal to 15%.
03:21
So 15 % is nothing but this is 0 .15%.
03:25
Remember this is for each engine, right? that is why i'm writing one engine out of four, right? remember, this is, we are talking about one engine, right? so probability, we are calculating for one engine right now.
03:42
Probability of chance of no engine failure, right? that means you can say this is one engine out of one out of four and we have here zero out of four engines.
04:15
Can you write this? yes, this is what it is implying here.
04:19
Okay, so now we know that the sum of happening of event plus some, you can say some of happening of event, that is failure is happening for one engine, right? and there is no failure.
04:38
So when you add these probabilities, you must be getting this probability as equals to 1.
04:44
So can you write 1 minus this value as probability of chance of no engine failure, failure? can be written as 1 minus 0 .15.
04:53
I'm sorry, i have written here 0 .15%.
04:56
I'm so sorry.
04:57
So here it comes out to be 0 .85, right? so this we have got.
05:04
Right.
05:04
So now this is becoming very complex, right? you must be getting very complex value.
05:10
So now let me just make here engines, right? let me just suppose there are four engines, right? there are four engines right so this is what we have calculated for one engine failure we will we have written 0 .15 and for no engine failure it is 0 .85 so what will be the probability probability that is p we have written exactly one engine failure exactly one engine failure isn't it so how is is it possible from these two four engines let me just write one two three four engine number one two three four right so we want only one failure right so this could be possible when there could be one condition would be what there could be either or condition right so when when this fails suppose let us say there are uh let me just write here somewhere else okay okay i will write here this is okay, let me just make a block here.
06:31
Okay, let me just tell you.
06:32
Okay, so first condition could be what? let us just say this fails, right? for the first time...