Q.6. Use the binomial distribution in which n = 6 and p = 0.3 to calculate the following probabilities: (a). x is at most 1. (b). x is at least 2. (c). x is more than 5. (d). x is less than 6. Solve all questions
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- Please give solution in correct and step by step answer format thanku Explaniation Please!!! Five people go to the supermarket to buy milk. Each person is equally likely to select (independently) from ten different brands available. Find the probability that they each select: (a) A different brand. (b) The same brand.Two cards are drawn from a standard deck without replacement. What is the probability that the first card is a diamond and the second card is red? (Round your answer to three decimal places.)A restaurant manager classifies customers as regular, occasional, or new, and finds that of all customers 50%, 40%, and 10%, respectively, fall into these categories. The manager found that wine was ordered by 70% of the regular customers, by 50% of the occasional customers, and by 30% of the new customers.a. What is the probability that a randomly chosen customer orders wine?b. If wine is ordered, what is the probability that the person ordering is a regular customer?c. If wine is ordered, what is the probability that the person ordering is an occasional customer?
- A biometric security device using fingerprints erroneously refuses to admit 3 in 1,500 authorized persons from a facility containing classified information. The device will erroneously admit 3 in 1,005,000 unauthorized persons. Assume that 98 percent of those who seek access are authorized. If the alarm goes off and a person is refused admission, what is the probability that the person was really authorized?You are modeling a qualitative variable that takes on two classes (classes 1 and 2). In trying to classify observation 11 (out of 20) you compute the conditional probability for class 1 as 0.51. How would you classify this observation?Half of a set of the parts are manufactured by machine A and half by machine B. Five percent of all the parts are defective. Five percent of the parts manufactured on machine A are defective. Find the probability that a part was manufactured on machine A, given that the part is defective.
- Please do not give solution in image format thanku Two Manufacturers supply food to a large cafeteria. Manufacturer A supplies 40% of the soup served in the cafeteria, while Manufacturer B supplies 60% of the soup that is served. 3% of the soup cans provided by Manufacturer A are found to be dented, while 1% of the cans provided by Manufacturer B are found to be dented. Given that a can of soup is dented, find the probability that it came from Manufacturer B.Suppose that there are two types of workers: high and low. Employers cannot distinguish between different types during an interview. Employers value high type at $200,000 and low type at $100,000. Employers are in a competitive market (i.e. zero profit applies). High type workers have a reservation wage of 140,000 and low type workers have a reservation wage of 80,000. Suppose that 50% of all workers are high type. The productivities, reservation wages, and the probabilities are common knowledge). What wage would the employers offer? Please explain the solution!In the game of blackjack as played in casinos in Las Vegas, Atlantic City, and Niagara Falls, as well as in many other cities, the dealer has the advantage. Most players do not play very well. As a result, the probability that the average player wins a hand is about 45%. Find the probability that an average player wins. a.Twice in 5 hands. b. Ten or more times in 25 hands. Arrivals 0 1 2 3 4 5 6 7 8 Frequency 14 31 47 41 29 21 10 5 2
- In the July 29, 2001, issue of The Journal News (Hamilton, Ohio), Lynn Elber of the Associated Press reported that “while 40 percent of American families own a television set with a V-chip installed to block designated programs with sex and violence, only 17 percent of those parents use the device.”(a)Use the report’s results to find an estimate of the probability that a randomly selected American family has used a V-chip to block programs containing sex and violence.find P(V and U)According to the report, more than 50 percent of parents have used the TV rating system (TV-14, etc.) to control their children’s TV viewing. How does this compare to the percentage using the V-chip?Given a binomial distribution, n = 6 and π = .25. Determine the probability given x = 2 using the binomial formula.In the CRRA utility family u(x) = x^(1−γ). If this individual has autility where γ = 0.01, would he prefer the payment of $320 or the gamble?