MAT119 - HW #7 Name: Please show all necessary work. Full credit will not be given if proper work is not shown. 1. The American Heart Association reported that, for people 18 years of age or older in the United States, an estimated 24.8 million men (23.1%) and 21.1 million women (18.3%) are cigarette smokers. Find the probability that a randomly selection person 18 years of age or older in the United States is a cigarette smoker. Assume one half the population is male. 2. A hospital billing department knows that the probability patients 60 or older pay the balance of their bill after one billing is 80%, while for a person under the age of 60 the probability is 45%. Seventy percent of the hospital's patients are 60 years or older. a. What is the probability the balance is paid after one billing? b. The balance of the bill is not paid after one billing. What is the probability the patient was 60 years or older? 3. [BONUS] Consider the following labelled graph. Suppose you have T different colors. In how many ways can you color the vertices of the tetrahedron assuming you start at vertex A (and proceed in alphabetical order) and no pair of vertices connected by an edge may share the same color? 4. Problems #19, 24 on pg. 442 and #29, 33, 37 on pg. 454-455