
Conditional Probability
Hey,
I'm having some real trouble trying to comprehend this problem.
A wholesale supplier classifies delivery jobs as small or large according to the amount of delivery space they require. As orders arrive at the supplier they are initially estimated to be small or large to provide some guidance in management. The company has found that 30% of its orders actually fall into its “large” classification. The initial estimation of orders is 90% reliable for large orders (i.e. the probability that a large order is initially allocated correctly to “large” is 0.9) but only 75% reliable for small orders.
(i) What proportion of orders is initially estimated as “large”?
(ii) Find the probability that a job which is initially estimated
as large is actually large.
Any help will be kindly appreciated.