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1. (Geometric) A medical team randomly selects people in an area, until he finds a person who has a corona virus. Let p is the probability that he succeeds in finding such a person, is 0.2 and X denote the number of people asked until the first success. (i) What is the probability that the team must select 4 people until he finds one who has a corona virus? (ii) What is the probability that the team must select more than 6 people before finding one who who has a corona virus?

1. (Geometric) A medical team randomly selects people in an area, until he finds a person who has a corona virus. Let p is the probability that he succeeds in finding such a person, is 0.2 and X denote the number of people asked until the first success. (i) What is the probability that the team must select 4 people until he finds one who has a corona virus? (ii) What is the probability that the team must select more than 6 people before finding one who who has a corona virus?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Problems 1. (Geometric) A medical team randomly selects people in an area, until he finds a person who has a corona virus. Let p is the probability that he succeeds in finding such a person, is 0.2 and X denote the number of people asked until the first success. (i) What is the probability that the team must select 4 people until he finds one who has a corona virus? (ii) What is the probability that the team must select more than 6 people before finding one who who has a corona virus? 2. (Negative binomial) Suppose 40% of employees at a firm have traces of asbestos in their lungs. The firm is asked to send 3 of such employees to a medical center for further testing. Find the probability that exactly 10 employees must be checked to find 3 with asbestos traces. What is the expected number and variance of employees that must be checked? binomial 3. (Negative binomial) If the probability is 0.40 that a child exposed to a certain contagious disease will catch it, what is the probability that the tenth child exposed to the disease will be third to catch it? 4. (Hypergeometric distribution) In the manufacture of car tires, a particular production process is known to yield 10tyres with defective walls in every batch of 100 tires produced. From a production batch of 100 tires, a sample of 4 is selected for testing to destruction. Find: (i) the probability that the sample contains 1 defective tire; (ii) the expectation of the number of defectives in samples of size 4; (iii) the variance of the number of defectives in samples of size 4. 5. Suppose 2% of items produced from an assembly line are defective. If we sample 10 items, what is the probability that 2 or more are defective? Here the count follows the binomial distribution. Suppose now that we sample 10 items from a small collection, like 20 items, and count the number of defectives. The resulting random variable is not binomial. Why not?
Transcribed Image Text:Problems 1. (Geometric) A medical team randomly selects people in an area, until he finds a person who has a corona virus. Let p is the probability that he succeeds in finding such a person, is 0.2 and X denote the number of people asked until the first success. (i) What is the probability that the team must select 4 people until he finds one who has a corona virus? (ii) What is the probability that the team must select more than 6 people before finding one who who has a corona virus? 2. (Negative binomial) Suppose 40% of employees at a firm have traces of asbestos in their lungs. The firm is asked to send 3 of such employees to a medical center for further testing. Find the probability that exactly 10 employees must be checked to find 3 with asbestos traces. What is the expected number and variance of employees that must be checked? binomial 3. (Negative binomial) If the probability is 0.40 that a child exposed to a certain contagious disease will catch it, what is the probability that the tenth child exposed to the disease will be third to catch it? 4. (Hypergeometric distribution) In the manufacture of car tires, a particular production process is known to yield 10tyres with defective walls in every batch of 100 tires produced. From a production batch of 100 tires, a sample of 4 is selected for testing to destruction. Find: (i) the probability that the sample contains 1 defective tire; (ii) the expectation of the number of defectives in samples of size 4; (iii) the variance of the number of defectives in samples of size 4. 5. Suppose 2% of items produced from an assembly line are defective. If we sample 10 items, what is the probability that 2 or more are defective? Here the count follows the binomial distribution. Suppose now that we sample 10 items from a small collection, like 20 items, and count the number of defectives. The resulting random variable is not binomial. Why not?
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