The population of voters in a hypothetical country was divided into income groups and also according to the presidential candidate they supported: a left-wing candidate, Gauche, and a right- wing candidate, Droite. Suppose the following table provides the joint probability distribution of income and candidate supported:
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- In a certain country, 47 percent of the population are on a strict diet. In a sample of 20 individuals, what is the probability that exactly 5 individuals are on a strict diet? Select one: O a. 0.1474 O b. 0.0260 O c. 0.1023 O d. 0.0577The percentage of mechanical-, civil-, aeronautical-, industrial-, and chemical-engineer- ing students in the course, Engineering Mathematics, is, respectively, 25, 20, 15, 22, and 18. The probability of a mechanical-, civil-, aeronautical-, industrial-, and chemical-en- gineering students getting the grade A is 0.7, 0.6, 0.8, 0.5, and 0.65, respectively. If a student chosen at random at the end of the semester earned an A in the course, find the probability of the student belonging to mechanical engineering.The population of a particular country consists of three eth- nic groups. Each individual belongs to one of the four major blood groups. The accompanying joint probability table gives the proportions of individuals in the various ethnic group-blood group combinations. Blood Group 0 A B AB 1 .082 .106 .008 .004 Ethnic Group 2 .135 .141 .018 .006 3 215 200 .065 .020 Suppose that an individual is randomly selected from the population, and define events by A = {type A selected}, B = {type B selected}, and C = {ethnic group 3 selected}. a. Calculate P(A), P(C), and P(AC). b. Calculate both P(A|C) and P(C|A), and explain in con- text what each of these probabilities represents. c. If the selected individual does not have type B blood, what is the probability that he or she is from ethnic group 1?
- A company sends its products from 3 warehouses, namely from warehouse A=30%, warehouseB=20% and from warehouse C=50%. Based on complaints from customers, it is known thatthe percentage of defective products sent from each warehouse is as follows: A=3% , B= 5% and from warehouse C= 2%.a. Suppose a customer after ordering the product, the next dayComplained that the item was defective. What is the probability that the product receivedthe customer is from warehouse C? b. If another customer who also orders the product and getsthe goods are in good condition, what is the probability that the product received by the customerdoes it come from warehouse A?An insurance company calculates car insurance premiums based on the age of the policyholder according to three age groups: Group A consists of drivers younger than 22 years old; Group B consistsof drivers 22—33 years old, and Group C consists of drivers older than 33 years.Its portfolio consists of 10% Group A policyholders, 38% Group B policyholdersand 52% Group C policyholders.The probability of a claim in any 12 month period for a policy belonging to GroupA, B or C is 13%, 3% and 2%, respectively.(i) Calculate the probability that a randomly chosen policy holder from thisportfolio will make a claim during a 12 month period. One of the company’s policyholders has just made a claim(ii) Calculate the probability that the policy holder is younger than 22 years.A random sample of 1000 adults has the elements of the sample classified by sex (= Male or Female) and educations ( = College, high School or Elementary). The results are summarized in the contingency table below. College High School Elementary Male 130 270 140 Female 170 180 110 Find the probability that a randomly selected person who is selected from the survey members is male, given that the individual finished college.
- A strand of patio lanterns has 10 identical lights. If one light in the strand fails to work, the entire strand of lights will not work. In order to have a 90% probability that the entire strand of lights will work, what is the maximum probability of failure for each individual light?A gas station has three grades of fuel, regular, premium and diesel. Due to problems with the supply chain, the probabilities that the station will run out of any three fuel types in a week are 0.10, 0.16 and 0.24, respectively. These probabilities are statistically independent. Also, if there is a shortage of diesel, the probability of a shortage of premium becomes 0.25. 1. How likely is the station to run out of all three fuels in a given week? 2. What is the probability that if regular runs out, both premium and diesel will also run out? 3. What is the probability that the station will run out of at least one of either premium and diesel? 4. What is the probability that the station will run out of at least 2 of the fuels in a week?An insurance company calculates car insurance company calculates car insurance premiums based on the age of the policyholder according to three age groups: Group A consists of drivers younger than 22 years old; Group B consists of drivers 22—33 years old, and Group C consists of drivers older than 33 years.Its portfolio consists of 10% Group A policyholders, 38% Group B policyholders and 52% Group C policyholders. The probability of a claim in any 12 month period for a policy belonging to Group A, B or C is 13%, 3% and 2%, respectively. (i) Calculate the probability that a randomly chosen policy holder from this portfolio will make a claim during a 12 month period. One of the company’s policyholders has just made a claim(ii) Calculate the probability that the policy holder is younger than 22 years.