Question

A fair die is rolled and the following events are considered:

1) A fair die is rolled and the following events are considered:  

A is the event that the outcome is an even.  

B is the event that the outcome is no more than2. 

C is the event that the outcome is greater than or equal to 4. 

Answer the following questions: 

(a) List the sample space and events A, B and C. 

(b) Find P(A), P(B) ad P(C) 

(c) Are A and B independent? Show your work. 

(d) Are A and C independent? Show your work. 

(e) Find the probability of B given C. Show your work. 


2) For the following statements, identify whether they are true or false:

(a) Two independent events are always disjoint. 

(b) A density curve should always be greater than zero 

(c) Two disjoint events are always independent. 

(d) Probability of an event is always greater than zero and less than 1.



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