## Question 770:

1## Answer:

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The easiest way to solve conditional probability problems is to construct a tree-diagram. It makes it easier to work backwards and forwards to answer the questions. I've attached the tree diagram in a word document.We need to use Bayes Theorem to solve this. But first we need to find the probability of a passing grade in order to find whether he completed the assignment.From the tree-diagram we follow the branches that get us to a passing grade.That is you can complete and pass or not complete and pass. We can see the probability of passing grade is then .80*.90 + .20*.60 = .72+.12 = .84

Using Bayes Theorem, the probability of completing the assignment, given a passing grade is :

P(Complete) * P(Passing | Complete) / P(Passing) = (.80 * .90) / .84 = .72/.84 = .8571 probability he completed the assignment given he received a passing grade.