1. In a drawer, I have five batteries three that work and two that do not work. If I grab three batteries, what is the probability that only one works. 2. . You are provided with the following information P(A) = 0.3, P(B) = 0.2, P (A OR B) = 0.44 and that the events are independent. What is P (A | B)? A school offered blood pressure screening for its employees. The results are shown in the table. a. We choose an employee at random, what is the probability that this person is a 30 to 49-year-old with normal blood pressure? Write the question also in function notation along with the appropriate mathematical symbols, equal signs, to communicate your work. Age Under 30 PressureBlood 3. 30 49 Over 50 Total Low 122 432 300 854 Normal 501 122 205 828 High 250 102 151 503 Total 873 656 656 2185 b. If an employee is over the age of 50, what is the probability that their blood pressure is high? Write the question also in function notation along with the appropriate mathematical symbols, equal signs, to communicate your work. c. Are the events a person is Over 50; a person has high blood pressure independent events? You must show work that leads to the conclusion that yes, the events are independent, or no, the events are not independent along with the statement whether the events are independent or not. Approximate to three decimal places to make your conclusion. 4. Comparison studies, such as which battery last longest or which aspirin works the best, makes one assumption as to what reality looks like. The assumption is that we have equality among the items we are comparing that is the items are equally good. What follows is the start of the model that is eventually constructed. Consider the random variable X which measures the weight of a coconut. The mean weight is 1.44 kg, and standard deviation of 0.23 kg. I randomly choose two coconuts, measure their weight individually, then subtract the weight; S = X - X. a. Find the value of E(S) = b. Find the value of SD(S) = 5. In a particular state university, 42% of students major in STEM fields (Science, Technology, Engineering and Mathematics). Of the students majoring in STEM fields 44% graduate in four years or less, while 52% of students in non-STEM related fields graduate in four years or less. a. What is the probability that a student chosen at random graduates in four years or less. b. If a student takes more than four years to graduate, what is the probability that they majored in a STEM field? c. Find P(Graduate 4 | Non-stem field) = d. What is the probability that a student chosen at random is in a STEM field and takes more than four years to graduate? 6. In Iceland 56% of the population hast O type blood. If four people are chosen at random what is the probability that at least one person has O type blood in the sample of four? 7. Motor vehicles sold to individuals (non-commercial) in the U.S. are classified as either cars or light trucks (Light does not mean small, but rather that it is not a commercial truck. For example, an SUV is considered a light truck) and as either domestic or imported. In early 2004, 69% of vehicles sold were light trucks, 78% were domestic, and 55% were domestic light trucks. a. Write the probability of 55% using function notation and the correct conjunction. b. A vehicle is chosen at random, what is the probability that it is domestic but not a light truck? 8. You roll a six-sided fair die. If it comes up a 6, you win $100 and that ends the play. However, if your first throw is not a 6 you get to roll again. If on the second throw you get a 6, then you win $50 and that ends the play. If you don't roll a six on the second roll you lose $25, and the play ends. Let the random variable Y equal the amount of money won or lost on one play (a play consists of rolling the die until you win or lose money). Create a probability table for all the outcomes of the random variable Y. Y P(Y = y) 9. If I toss a die four times what is the probability that it lands on six all four times