The probability that the error occurred when Engineer 2 made the mistake is 0.462 on the other hand the probability that the error occurred when the engineer 1 made the mistake is 0.538
Explanation:
Let denote the event that the 1st engineer does the work.so we write
=0.7
Let denote the event that the 2nd engineer does the work .So we write
=0.3
Let O denote the event during which the error occurred .so we write
=0.02(GIVEN)
=0.04(GIVEN)
- The probability that the error occurred when the first engineer performed the work is
- The probability that the error occurred when the first engineer performed the work is
Now we need to find when did the error in the work occur so we will compare the probability of the work done by <u>engineer 1 </u>and <u>engineer 2 </u>
<u></u>
<u>lets find the Probability of the Engineer 1</u>
<u>Using Bayes theorem,we get</u>
<u></u>
<u></u> =0.02*0.7/0.02*0.7+0.04*0.3 = 0.014/0.026=0.538
<u>lets find the Probability of the Engineer 2</u>
<u></u> =0.04*0.3/0.02*0.7+0.04*0.3=0.012/0.026=0.462
Since ,0.462<0.538 so it is more prominent that the Engineer 1 did the work when the error occurred