00:01
Hello students, today we will discuss about this question.
00:03
In this question we are given that in a bolt factory machine a, b, c, respectively produced 20 percentage, 30 percentage and 50 percentage of the total output of the respective outputs, that is 5%, 3 percentage and 2 percentage that are defective.
00:28
Now a bolt is selected at a random then in the part a we need to calculate the probability that it is defective.
00:40
So here we need to find p of d that is equal to question mark and in the part b we need to give this is we are given that d is defective and compute the probability that was made by machine a.
00:56
So therefore here we need to find the probability of a given d is equal to question mark.
01:04
So here first of all, here we can say the probability of a is equals to 0 .2, probability of b is equals to 0 .3 and probability of c is equals to 0 .5.
01:18
Now for the part a, probability of defective, that is p of d, is equals to probability of a, intercept, d, plus probability of b intersection d, plus probability of c intersection d.
01:34
So that is equal to probability of d divided by a, multiplied by probability of a, plus probability of d divided by b, d given b, multiplied by probability of b, plus probability of d given by c, multiplied by probability of c.
01:56
So that is equal to 0 .05 multiplied by 0 .2 plus 0 .03 multiplied by 0 .3 plus 0 .02 multiplied by 0 .5...