A student is taking a standardized test consisting of several multiple-choice questions. One point is awarded for each correct answer. Questions left blank neither receive nor lose points. There are eight options for each question and the student is penalized 1 6 point for each wrong answer. Is it in the student's best interest to guess? Explain. Determine if it is in the best interest of the student to guess and explain your answer using the expected value. Choose the correct answer below. (Round to two decimal places as needed.) OA. No, the student should not guess because the expected value is OB. Yes, the student should guess because the expected value is OC. The student will have no loss or gain by guessing because the expected value is K For the past several years, a fire department has been keeping track of the number of fire hydrants that have been opened illegally daily during the heat waves. These data (rounded to the nearest 10) are given in the table below. Use this information to calculate how many hydrants the department should expect to be opened per day during the upcoming heatwave. The expected number of fire hydrants opened is (Round to the nearest whole number as needed.) Hydrants Opened Days 40 234567 20 10 30 10 11 50 12 60 70 603 A card is drawn from a standard 52-card deck. Calculate the expected value for the game. A player must pay 6 dollars to play the game, which must be subtracted from the winnings. If a heart is drawn, the player wins 9 dollars; otherwise, they lose their 6 dollars. Calculate the price that would make the game fair. The expected value of this game is dollars. (Round to the nearest cent as needed.) + A certain game consists of rolling a single fair die. If a four or five comes up, you win 10 dollars; otherwise, you lose 5 dollars. Fine the expected winnings for this game. Is this a fair game? The expected value for this game is dollars. ABCDE To the right are the probabilities and values associated with five outcomes Outcome of an experiment. Calculate the expected value for the experiment. The expected value for this experiment is (Round to the nearest tenth as needed.) Probability 0.1 Value 0.1 0.2 -1 0.2 A college administration has conducted a study of 200 randomly selected students to determine the relationship between satisfaction with academic advisement and academic success. They obtained the following information. Of the 72 students on academic probation, 41 are dissatisfied with advisement; however, only 29 of the students not on academic probation are dissatisfied with advisement. What is the probability that a randomly selected student is not on academic probation? The probability that a randomly selected student is not on academic probation is . (Type a decimal rounded to two decimal places as needed.) K A company estimates that it has a 5% chance of being successful in bidding on a $59,000 contract. If it costs $5,400 in consultant fees to prepare the bid, what is the expected gain or loss for the company if it decides to bid on this contract? for the company of $. There is an expected (Type an integer or a decimal.) If P(AUB)=0.8, P(A) = 0.5, and P(ANB) = 0.15, find P(B). Assume that A and B are events. P(B) = (Simplify your answer. Type an integer or a decimal.) What is the probability of getting either a club or a king when drawing a single card from a deck of 52 cards? The probability that the card is either a club or a king is (Simplify your answer. Type a fraction.) A pair of dice is rolled. What is the probability of getting a sum less than 8? What is the probability of getting a sum less than 8? (Type an integer or simplified fraction.) A pair of dice is rolled. What is the probability of getting a sum less than 8? What is the probability of getting a sum less than 8? (Type an integer or simplified fraction.) If there is a 1 in 3,000 chance that you will pick the numbers correctly in tonight's lottery, what is the probability that you will not pick the numbers correctly? The probability you will not pick the correct numbers is . (Type an integer or simplified fraction.) You want to purchase a DVD drive for your laptop computer. Assume that 65% of the drives are made outside of the United States. Of the U.S.-made drives, 4% are defective; of the foreign-made drives, 7% are defective. If your drive is defective, find the probability that it is foreign made. The probability is (Do not round until final answer. Round to three decimal places as needed.) Find the probability, P(QNR), associated with the tree diagram. What is P(QNR)? (Round to the nearest hundredth.) 0.1 M 0.6 N 0.7 R 0.3 S 30 0.2 R 0.8 S Q 0.3 0.6 R 0.4 S The given urn contains green (G), blue (B), and B G red (R) balls. Assume that two balls are being drawn without replacement from the urn to the right. B G What is the probability that neither ball is red? BG The probability is (Type an integer or decimal rounded to three decimal places as needed.) The (hypothetical) table below shows the relationship between the number of hours students work at part-time jobs each week and the number of years it takes then to graduate with an undergraduate degree. If a student works more than 20 hours per week, what is the probability that the student graduates in 4 years? Amount of Hours 4 Years 5-6 Years Over 6 Years Totals Worked per Week 0-5 192 55 28 275 6-20 142 76 38 256 Over 20 Totals 83 118 41 242 417 249 107 773 The probability is (Type an integer or decimal rounded to three decimal places as needed.) + A certain game consists of rolling a single fair die. If a four or five comes up, you win 10 dollars; otherwise, you lose 5 dollars. Fine the expected winnings for this game. Is this a fair game? The expected value for this game is dollars.