A study is conducted to assess the impact of caffeine consumption, smoking, alcohol consumption, and physical activity on the risk of cardiovascular disease. Suppose that 40% of participants consume caffeine and smoke. If 8 participants are evaluated, what is the probability that: Exactly half of them consume caffeine and smoke?

Enterococci are bacteria that cause blood infections in hospitalized patients. One antibiotic used to battle enterococci is vancomycin. A study by the Federal Centers for Disease Control and Prevention revealed that 3% of all enerococci isolated in hospitals nationwide were resistant to vancomycin. Suppose 18 patients with blood infections caused by the enterococci bacteria and treated with vancomycin are randomly selected. Rounding your answer to four decimal places, find the probability that all 18 patients will be successfully treated 0.97 x at least one patient will not be successfully treated 0.422✓

A country has a population of 21M people. Some people received a certain treatment and some didn’t. Table 1 shows the disease rates based on age and treatment status. The treatment has no side effects, and only changes the probability that someone contracts this (undesirable) disease. Age Untreated Treated People Disease Disease per 100K People Disease Disease per 100K young 5,000,000 40 0.8 5,000,000 20 0.4 old 1,000,000 60 6.0 10,000,000 300 3.0 Table 1: Disease rates based on age and treatment status. (a) Define the following events and compute four conditional probabilities of contract- ing the disease based on a person’s age and based on their treatment status. The events are D:= contracting the disease, Y := young, O:= old, T:= treated, and U:=untreated. Note that O = Y c, and similarly for T and U. Now, calculate 4 probabilities like P(D|T, Y ) for each possibility. (b) What is the probability of contracting the disease if you are treated? Untreated? (c) Based on…

In a 1 pond bag of skittles the possible colors were red, green, yellow, orange, and purple. The probability of drawing a particular color from that bag is given below. Is this a probability model? Answer Yes or No. Color Probability Red 0.2291 0.1902 Green Orange Yellow Purple A. No B. Yes 0.2163 0.1884 0.1815