I was solving a probability question. Here are the screenshots for the problem.
I want to know , In the second image when we are calculating P(D | E1) , why it is being divided by 100. The sample space for E1 is 25% , then why are we dividing by 100.
P( D | E1) = P( D intersection E1)/ P( E1)
Why don't we use this formula here?
I have tried to ask on many forums but still could not clear my doubt.
$\mathsf P(D\mid E_1)$ is the probability that a bolt is defective given that it is produced by factory $A$.
You are told that "of their respective outputs $\bf 5\%$, $4\%$, and $2\%$ are defective".
Hence these are the probabilities that a bolt is defective when given that it is from a specified factory.
Thus no calculation is required. $\qquad$ $\mathsf P(D\mid E_1)=5\%\\\mathsf P(D\mid E_2)=4\%\\\mathsf P(D\mid E_3)=2\%$