Random Probability Review

An insurance company charges $800 annually for car insurance. The policy specifies that the company will pay $1000 for a minor accident and $5000 for a major accident. If the probability of a motorist having a minor accident during the year is .2, and having a major accident, .05, how much can the insurance company expect to make on a policy? Complete the probability distribution table. Start with the lowest x value to the highest. x -4200 -200 800 P(x) .05 .2 .75 From the above question... An insurance company charges $800 annually for car insurance. The policy specifies that the company will pay $1000 for a minor accident and $5000 for a major accident. If the probability of a motorist having a minor accident during the year is .2, and having a major accident, .05, how much can the insurance company expect to make on a policy? How much can the insurance company expect to make on a policy? A dealer in the Sands Casino in Las Vegas selects 40 cards from a standard deck of 52 cards.Let Y be the number of red cards (hearts or diamonds) in the 40 cards selected. Which of the following best describes this setting: Y has a binomial distribution with n = 40 observations and probability of success p = 0.5. Y has a binomial distribution with n=40 observations and probability of success p = 0.5, provided the deck is shuffled well. Y has a binomial distribution with n=40 observations and probability of success p = 0.5, provided after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected. Y has a normal distribution with mean p = 0.5. Y has a normal distribution with mean p = 0.5. ) In a certain large population, 40% of households have a total annual income of over $70,000. A simple random sample is taken of 4 of these households. Let X be the number of households in the sample with an annual income of over $70,000 and assume that the binomial assumptions are reasonable. What is the mean of X? 1.6 28,000 0.96 2, since the mean must be an integer The answer cannot be computed from the information given. A department store has a promotion in which it hands out a “scratch card” at the checkout register, with a percent discount concealed by an opaque covering. The customer scratches off the covering and reveals the amount of the discount. The table below shows the probability that a randomly selected card contains each percent discount.What is the expected value of the discount? 5% 12% 15% 21% 40% In the casino game of roulette, there are 38 slots for a ball to drop into when it is rolled around the rim of a revolving wheel: 18 red, 18 black, and 2 green. What is the probability that the first time a ball drops into the red slot is on the 8th trial? Recall that there are 4 suits - spades, hearts, clubs, and diamonds - in a standard deck of playing cards. Suppose you play a game in which you draw a card, record the suit, replace it, shuffle, and repeat until you have observed 10 cards. Define X = numbers of spades observed.a) Show that X is a binomial random variable.b) Find the probability of observing fewer than 4 hearts in this game.c) Find the expected value and standard deviation of this binomial and interpret it in context. Suppose that 20% of Super Crunch cereal boxes contain a secret ring. Let X = the number of boxes of Super Crunch that must be opened until a ring is found.a) Show that X is a geometric random variable.b) Find the probability that you will have to open 7 boxes to find a ring.c) How many boxes would you expect to have to open to find a ring?