## If a man tests negative, what is the probability that he actually has the disease?

1.  Refer to Example 2.26.

a.  If a man tests negative, what is the probability that he actually has the disease?

b.  For many medical tests, it is standard procedure to repeat the test when a positive signal is given. If repeated tests are independent, what is the probability that a man will test positive on two successive tests if he has the disease?

c.   Assuming repeated tests are independent, what is the probability that a man tests positive on two successive tests if he does not have the disease?

d.  If a man tests positive on two successive tests, what is the probability that he has the disease?

2.  If A and B are independent events, prove that the following pairs of events are independent: A c and B, A and B c , and A c and B c .

3.   A fair die is rolled twice. Let A be the event that the number on the first die is odd, let B be the event that the number on the second die is odd, and let C be the event that the sum of the two rolls is equal to 7.

a.  Show that A and B are independent, A and C are independent, and B and C are independent. This property is known as pairwise independence.

b.  Show that A, B, and C are not independent. Conclude that it is possible for a set of events to be pairwise independent but not independent. (In this context, independence is sometimes referred to as mutual independence.)

### Determine the outlet concentration x1 in the water solution and in the trichloroethane solution using an analytical equation.

Predicting Extraction for an Existing Tower with a Given Number of Steps. An existing tower contains 5.0 theoretical steps. It is desired to predict its performance under the following conditions….

### Calculate the minimum solvent that can be used. [Hint: In this case, the tie line through the feed L0 represents the condition for minimum solvent flow rate.

Minimum Solvent and Countercurrent Extraction of Acetone. An aqueous feed solution of 1000 kg/h containing 23.5 wt % acetone and 76.5 wt % water is being extracted in a countercurrent….

### Determine the break-point time, the fraction of total capacity used up to the break point, the length of the unused bed, and the saturation loading capacity of the solid.

Drying of Nitrogen and Scale-Up of a Column. Using molecular sieves, water vapor was removed from nitrogen gas in a packed bed (C1) at 28.3°C. The column height was 0.268….