A certain reliability defect can be detected only with a destructive test. However ...

Part I:

A bowl contains 10 jelly beans. Half of the jelly beans are red, and the other half are green. If you randomly select 3 jelly beans,

1. What is the probability that they are all green?
2. What is the probability that one is green?

Part II:

A certain reliability defect can be detected only with a destructive test. However, quality control has developed a nondestructive test that the product that has the defect will fail the test 95% of the time. Those without the defect pass the test 95% of the time. Quality control proposes using the test as a 100% screening on all of the products. Products that fail the screening will not be replaced. 

• If 2% of the product has the defect, what will be the      percent of defective products that will get passed the screening? 
  • First construct a table of the form below for listing       all the possible probabilities, where intersections, such as P(F) and       P(D) are found by finding P(F|D) * P(D), and so on. 
  • NOTE: P(F) gives the probability of failure of       the screening, P(F’) is not failure of the screening, P(D) is probability       the product is defective, and P(D’) is the probability the product is not       defective. Remember that the probabilities must sum to 1 in the       bottom right corner.