At Least 4 Successes In 6 Trials With P = 0.8

1. (1). At least 4 successes in 6 trials with p = 0. 8(2). At least 2 failures in 6 trials with p = 0. 32. Text involving the computation of probabilities for a Bernoullitrial. Assume that n = 10, and p =4/8. Find the probability of atleast 2 successes and at least 2 failures3. Assume that the coin is weighted so that a tail is 4 times aslikely as a head. The coin is flipped 12 times. What is the probability that both heads and tails occur4. Assume that 8 questions are answered by guessing. What is theprobability of at least 6 correct answers5. Good Vehicles, Inc. , auto dealer, assume that 1 car in 8 isdefective and will not start. If at different times 4 individuals eachrandomly select a car to test drive, what is the probability that atleast 1 of them selects a car that will not start6. Assume that a box contains 3 defective widgets and 8acceptable widgets. There are 4 inspectors, each of whom selectsa widget from the box at random, inspects it, and then replaces itin the box. Each inspector makes his or her inspection at adifferent time. What is the probability that at least one inspector will find adefective widget7. Assume that 35 percent of voters are Republicans, 35 percentare Democrats, and 30 percent are Independents. A poll takerasks 8 people at random for their party affiliation. Assume furtherthat, because the city is so large, this situation can beapproximated by a Bernoulli process. What is the probability that at least 5 of those polled areDemocrat voters?8. professor who sometimes forgets to bring her briefcase to theoffice, but assume that, each day, the probability that she forgetsthe briefcase is1/7. Assume that her forgetting is a Bernoulli process. (1) What is the probability that she remembers to bring herbriefcase every day in one week (5 days)?(2) What is the probability that she forgets to bring her briefcaseevery day in one week (5 days)?(3) What is the probability that she forgets to bring her briefcaseat least one day in one week (5 days)?9. a basketball player’s three point shooting. Assume that hisshots are Bernoulli trials, and that he makes 2 in 8 of his shots. How many three point shots must the player attempt so that theprobability of his hitting at least one of them is at least 0. 99?10. assume that the probability density function for the randomvariableXis the one given in the table below: Value of ProbabiliXty-40. 200. 310. 150. 4What is the expected value of E[X]=11. involving the expected value of a given probability densityfunction. Use the density function shown below instead of the onein your text. Value of ProbabiliXty6/16-52/16-323/163/1642/16-1What is the expected value of this probability density function?12. Assume that the drawer contains 14 coins: 5 quarters, 3dimes, and 6 nickels. One coin is randomly selected. What is the expected value of the coin selected (in cents)13. simultaneous and random selection of three balls from a box,but assume that the box contains 7 red balls and 5 blue balls. Therandom variable,Fill in the table below to complete the probability density functionof x,find the list values of x in ascending orderValue of X0123Probability