68. A salesman has a 60 per cent chance of making a sale to each customer. The behaviour of successive customers is independent. If two customers A and B enter, what is the probability that the salesman will make a sale to A or B ?
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- Assume that three stop lights on the way to school are independent. Their time probabilities are P(Red)=0.4, P(Green)=0.5, and P(Yellow)=0.1 values. What is the probability of getting ALL THREE green lights on a trip to school?QL: If Ali drive 4 sessions, he have a 60% chance of winning. Assuming that the sessions are independent of each other, what is the probability that: 1. Ali will win 0, 1,2.3 orall 4 sessions, 2. Ali will win at least one session. 3. Al will win a majority of the sessions.Ponderosa Paint and Glass carries three brands of paint. A customer wants to buy another gallon of paint to match paint she purchased at the store previously. She can’t recall the brand name and does not wish to return home to find the old can of paint. So, she selects two of the three brands of paint at random and buys them. What is the probability that she matched the paint brand? Her husband also goes to the paint store and fails to remember what brand to buy. So, he also purchases two of the three brands of paint at random. Determine the probability that both the woman and her husband fail to get the correct brand of paint. (Hint: Are the husband’s selections independent of the wife’s selections?)
- 1. A class of 18 pupils consist of 11 girls, 4 of whom are left-handed, and 7 boys, only one of whom is left-handed. The two pupils are to be chosen at random from the class to act as monitors. Calculate the probabilities that the chosen pupils will consist ofa. One girl and One boyb. One girl who is left-handed and one boy who is left-handedc. Two left-handed pupilsAt the close of the stock markets on a day in 2013, there were 5905 companies listed with a certain stock exchange. On this day, the probabilities of advancing, declining, and unchanged company stocks appears in the table for the two exchanges. Find the probability an unchanged stock was listed on Exchange 1. Exchange Exchange 1 Exchange 2 Percentage of Probability of Probability of Stock Stock Companies Listed Advancing Declining 0.045 0.267 0.047 0.297 54.4% 45.6% The probability that an unchanged stock was listed on Exchange 1 is (Round to three decimal places as needed.) Probability the Stocks Remain Unchanged 0.045 0.047In 2013, the total sales from 3 different car production companies was 606,334 cars or light trucks. The probability that the vehicle was made by Company A was 0.381, by Company B 0.350, and by Company C 0.258. Additionally, the probability that a Company A vehicle sold was a car was 0.385, a Company B vehicle sold was a car was 0.370, and a Company C vehicle sold was a car was 0.332. Given the vehicle sold was a car, find the probability it was made by Company A. The probability a vehicle was made by Company A, given it was a car is (Round to three decimal places as needed.)
- After a workday, you visit a bar from monday to friday. The bar offers four differrent beer flavors. Each day you select one flavor with the following probabilities: flavor 1 with 30% flavor 2 with 25% flavor 3 with 40% flavor 4 with a 5% What is the probability that the first time you eat flavor 3 is on tuesday?The management of the large department store in Example B.1 must determine whether more training is neededfor the customer service clerk. The clerk at the customer service desk can serve an average of three customersper hour. What is the probability that a customer will require 10 minutes or less of service?Q1. Some couples planning a new family would prefer at least one child of each sex. The probability that a couple’s first child is a boy is 0.512. In the absence of technological intervention, the probability that their second child is a boy is independent of the sex of their first child, and so remains 0.512. Imagine that you are helping a new couple with their planning. If the couple plans to have only two children: What is the probability that at least one girl is born?
- Ryuji Sakamoto wants to be voted Best Athlete and needs to earn the support of fellow athletes at his high school, Shujin Academy, before the election. He can talk with three groups of students: the track and field students, the volleyball team, and the baseball team. Assume every student fits into only one of these groups and that all students will vote. The size of each group and the chance that the group would vote for Ryuji are given below. Probability the Group will Vote for Ryuji Size of the Group Group (in percent of athletes) Track and Field 47% 76% Volleyball 33% 44% Baseball 20% 43% The percentage of votes Ryuji is expected to get is Number %. Is Ryuji expected to win? Yes O NoSuppose you’re playing Texas Hold ’Em Poker, and you are dealt a hand witha Jack of Clubs and a Queen of Hearts. The river of 5 cards hasn’t been dealtyet, and you’re hoping to get a straight (5 cards with consecutive ranks, such as10,J,Q,K,A or 8,9,10,J,Q). What is the probability that you will get a straightthat uses both the Jack and Queen in your hand? (This last part is to keep theproblem simple, since it’s possible to get a straight that uses neither card in your hand, suchas A,2,3,4,5, all in the river. Besides, in those cases, ALL players would have a straight, sothat’s not so good for you!)Guide: Our goal is to calculate:P(straight using both cards in hand) = # 5-card combinations that get us a straight with the J & Q# 5-card combinations overall .(a) We’ll start with the denominator, which can be done with a singleformula from class: How many 5-card combinations are possible for theriver? (Keep in mind what is in your hand. Note that how many opponents you haveand what…
