1. Consider the hospital emergency room data in Example 2-8. Let A denote the event that a visit is to hospital 4, and let B denote the event that a visit results in LWBS (at any hospital). Use the addition rules to calculate the following probabilities.
A) P(A Union B).
B) P(A Union B').
C) P(A' Union B').
2. Determine the following probabilities.
A) P (A|B).
B) P(A'|B).
C) P(A|B')
D) P(B|A).
E) P(A Intersection B).
F) Use the total probability rule to determine P(A).
3. Again, Let A denote the event that a visit is to hospital 4, and let B denote the event that a visit results in LWBS (at any hospital). Are these events independent? Explain.

The concept of conditional probability is applied here, probability been the likelihood of an event occurring. two events A and B are said to be mutually exclusive is one event precludes the happening of the other event i.e one is dependent on the other one occurring.

Conditional probability on the other hand is the happening of an event taking into consideration that an event had already happened.

Let P(A) and P(B) be the probability of event and B occurring.

P(A and B) is the probability of both A and B = P(A) x P(B)

P(A or B) = is the probability of either A or b = P(A union B)

as such, P(A union B) = P(A) + P(B) - P(A and B).

The steps and appropriate explanation is as shown in the attached file.