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1. A study has been done to determine whether or not a certain drug leads to an improvement in symptoms for patients with a particular medical condition. The results are shown in the following table.
   

   	Improvement	No Improvement	Total
   Drug	270	530	800
   No Drug	120	280	400
   Total	390	810	1200

   
   
   Based on this table, what is the (empirical) probability that a patient shows improvement if it is known that the patient was given the drug?
   1.   ?    .3375
   2.   ?    .225
   3.   ?    .325
   4.   ?    None of the answers given; click to see the solution.

2. The results of the study in question #1 on the relationship between a certain drug and the improvement in symptoms for patients with a particular medical conditon are repeated below.
   

   	Improvement	No Improvement	Total
   Drug	270	530	800
   No Drug	120	280	400
   Total	390	810	1200

   
   
   Suppose it is known that the patient shows improvement. Based on this table, what is the (empirical) probability that the patient was given the drug?
   1.   ?    .692
   2.   ?    .225
   3.   ?    .667
   4.   ?    None of the answers given; click to see the solution.

3. Two cards are drawn in succession from a standard 52-card deck. What is the probability that both cards are aces if the cards are drawn without replacement?

   1.   ?    .0045
   2.   ?    .0385
   3.   ?    .0059
   4.   ?    None of the answers given; click to see the solution.

4. A box contains four red, two white, and three green marbles, all of which are the same size. Two marbles are selected one after the other from the box, without replacement. What is the probability that the marbles are the same color?

   1.   ?    .28
   2.   ?    .67
   3.   ?    .014
   4.   ?    None of the answers given; click to see the solution.

5. A company has three plants at which it produces a certain item. 30% are produced at Plant A, 50% at Plant B, and 20% at Plant C. Suppose that 1%, 4% and 3% of the items produced at Plants A, B and C respectively are defective. If an item is selected at random from all those produced, what is the probability that the item was produced at Plant B and is defective?

   1.   ?    .02
   2.   ?    .2
   3.   ?    .04
   4.   ?    None of the answers given; click to see the solution.

6. A company has three plants at which it produces a certain item. 30% are produced at Plant A, 50% at Plant B, and 20% at Plant C. Suppose that 1%, 4% and 3% of the items produced at Plants A, B and C respectively are defective. If an item is selected at random from all those produced, what is the probability that the item is defective?

   1.   ?    .029
   2.   ?    .08
   3.   ?    .027
   4.   ?    None of the answers given; click to see the solution.

7. The results of the study in question #1 on the relationship between a certain drug and the improvement in symptoms for patients with a particular medical conditon are repeated below.
   

   	Improvement	No Improvement	Total
   Drug	270	530	800
   No Drug	120	280	400
   Total	390	810	1200

   
   
   Based on this table, are the events "has the drug" and "improvement" independent events?
   1.   ?    No, they are not independent.
   2.   ?    Yes, they are independent.