There m types of coupons. Each new coupon collected is of type i with probability pi, ATTL Pi 1. We collect n coupons independently. (1). Find the expectation of the number of type 1 coupon we get. (2). Find the expected number of distinct types we get.
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- QUESTION 2 a) Based on the past data, 8% of customers will order a dessert with the meal at a noodle's restaurant. 14% of them will order a bottled beverage. i. What is the probability that a customer will order both a dessert and a bottled average? (2 marks) ii. The customers have ordered a dessert with the meal. Calculate the probability that he or she will order a bottled beverage. (2 marks) b) The Graduate Management Admission Test (GMAT) is a requirement for all applicants of MBA programs. A variety of preparatory courses are designed to help applicants improve their GMAT scores, which range from 200 to 800. Suppose that a survey of MBA students reveals that among GMAT scorers at least 650, 72% took a preparatory course; whereas among GMAT scores of less than 650 only 31% took a preparatory course. The probability for an applicant to score at least 650 is 30%. Suppose he was not taking the preparatory course. What is his probability of achieving 650 or more for GMAT score? (5…Consider events A and B that are independent. Let P(A) = 0.2 and P(B) = 0.3. What is the probability that both events will occur? 0.006 O 0.28 0.06 0.3K Suppose a basketball player is an excellent free throw shooter and makes 92% of his free throws (i.e., he has a 92% chance of making a single free throw). Assume that free throw shots are independent of one another. Suppose this player gets to shoot three free throws. Find the probability that he misses all three consecutive free throws. Round to four decimal places. OA. 0.2213 OB. 0.9995 OC. 0.0005 OD. 0.7787
- The genotype of an organism can be either normal (wild type, W) or mutant (M). Each generation, a wild type individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005 of having a wild type offspring.Timely patching is important for server security. Suppose an organization has 3 servers. Two of them have been patched, while one of them still remains unpatched. The prob- ability an unpatched server gets compromised is, and the probability that a patched server get compromised is p. If an attacker randomly attacks one of the three servers, the probability he compromises the server is (a) What is the value of p? • (b) This time the attacker randomly chose two servers to attack, and observed only one of them got compromised. What is the conditional probability that both attacked servers are patched?A man wants to adopt a puppy from an animal shelter. At the shelter, he finds eight puppies that he likes, a male and female puppy from each of the four breeds of water spaniel, chow chow, collie, and Labrador. The puppies are each so cute that he cannot make up his mind, so he decides to pick the dog randomly. Find the probability that the man chooses a male puppy. E The probability of choosing a male puppy is. (Type a simplified fraction.)
- Assume that n 16, and p = 9/10. Find the probability of at least 2 successes and at least 3 failures.D. 1/2 295: ECE Board March 1996 The probability of getting a credit in an examination is 1/3. If three students are selected at random, what is the probability that at least one of them got a credit? ring A. 19/27 B. 8/27 C. 2/3 D. 1/3The probabilities that a service station will pump gas into 0, 1, 2, 3, 4, or 5 or more cars during a certain 30 – minute period are 0.03, 0.18, 0.24, 0.28, 0.10, and 0.17. Find the probability that in this 30 – minute perioda. More than 2 cars receive gas;b. At most 4 cars receive gasc. 4 or more cars receive gas
- 5c The genotype of an organism can be either normal (wild type, W) or mutant (M). Each generation, a wild type individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005 of having a wild type offspring. Calculate the probability of a string of the following genotypes in successive generations: WWW.Factories A and B produce computers. Factory A produces 2 times as many computers as factory B. The probability that an item produced by factory A is defective is 0.033 and the probability that an item produced by factory B is defective is 0.031. What is the probability that a computer comes from Factory A?Answer:A computer is selected at random and it is found to be defective. What is the probability it came from Factory A?Answer:K Suppose there is a 22.1% probability that a randomly selected person aged 30 years or older is a smoker. In addition, there is a 24.3% probability that a randomly selected person aged 30 years or older is male, given that he or she smokes. What is the probability that a randomly selected person aged 30 years or older is male and smokes? Would it be unusual to randomly select a person aged 30 years or older who is male and smokes? The probability that a randomly selected person aged 30 years or older is male and smokes is Would it be unusual? O Yes O No www (Round to three decimal places as needed.). wew
