00:01
Hello students, we are going to write here for this 100 cars are enter for roadworthiness.
00:07
So basically which is in two parts, mechanical and electricals.
00:10
So basically a car passes only if it passes both parts.
00:14
So if i write here half the car failed the mechanical test in 62 pass mechanical, 15 pass the electrical but fail the mechanical test.
00:24
Fine, we are going to find the probability that the car chosen at random passes overall fails on one test.
00:30
Only given that it has failed the mechanical test only so if i write here for this here here we are writing here x and y x and y denote if i write here for this the events of the events the events of cars undergoing undergoing we are going we are going to write here for this this must be written as under going mechanical and electrical test mechanical and electrical if i write here for this this must be test so basically if i write here for this this is so if i write here for this what would be our probability of x which represents our mechanical this is 0 .50 divided by 100 half so basically this is 0 .5 and probability of y that is equivalent to 65 divided by 100 which is 0 .6 if i write here for this and so probability of a intersection b dash is given as 15 divided by 100 this is according to the information given in the question 0 .15 so definitely using formula a intersection b dash is given would be p of a minus we are going to write here for this p of a intersection b dash which is 0 .5 so basically a here is x and b here is y so we can write here according to the terms written in x and y so this is also x and y we are going to write here x y x y we are going to write here x y x y x and y so 0 .5 minus 0 .15.
02:37
So this must be written as 0 .35.
02:42
So basically if i write here for this, this is probability of x intersection.
02:51
We are writing here.
02:53
So probability of x dash intersection y must be equivalent to probability of x minus probability of x intersection y so this must be equivalent to 0 .6 of 5 minus 0 .3 5 that must be equivalent to 0 .3 so basically if i write here for this we are writing here in the first case find the probability that car chosen at random passes overall fails on one test so if i write here for this so what we need to find here probability we are writing here probability of a car chosen at random we are going to write here for this random given given that it has failed so let's erase this to make it more clear given that it has it has failed we are writing here this must be written as failed the mechanical test only we are going to write here mechanical test only so basically if i write here for this this must be probability of b -dast so we are going to take a dash which means that x -dice divided by x -des intersection so this must be must be s -test intersection y -dess.
04:42
So in the bracket we can calculate right here something here.
04:46
The probability, the probability, if i write here for this of field dot test, field dot test, that must be equivalent to we are going to write here probability of x -dash union y -dess, x dash union y dash that must be equivalent to if i write here for this this is probability of this must be probability one minus probability of x intersection y so this must be 1 minus 0 .35 this must be 1 minus 0 .35 that must be equivalent to so if i write here 1 minus 0 .35, that must be equivalent to 0 .65...