Suppose that 40% of all adults regularly consume coffee, 50% regularly consume carbonated soda, and 75% regularly consume at least one of these two products.(a) What is the probability that a randomly selected adult regularly consumes both coffee and soda?(b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?

Introduction: Probability of intersection of two events: Probability of intersection of two events…

Answered: Suppose that 40% of all adults…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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3) Approximately 25 % of American men in their 50’s have prostate cancer. High levels of prostate specific antigens (PSA) in blood is used as a test for prostate cancer. Approximately 20% on men with prostate cancer have a normal PSA level and two out of three men without prostate cancer have high PSA levels. Calculate the probability that a PSA test on an American in his 50’s will result in a false positive.
Suppose that in the small state of Rhode Island in the USA, the average number of women suffering severe osteoporosis (due to the consumption of dairy products) in any given month is 12. What is the probability that in just one-quarter of a month there will be eight (8) women found suffering severe osteoporosis?
Only 6% of people has 0-negative blood type. If a local blood drive has 100 donors, what is the probability that at least 10 of the 100 donors has O-negative blood?
Detecting terrorists is a real problem, one that causes governments to spend millions per year. A particular surveillance system has been developed which correctly identifies a future terrorist 99% of the times and detects someone who is not a future terrorist 99.9% of times. Suppose that in a population of 300 million, there are 1000 potential/future terrorists. If one of these 300 million is randomly selected and scrutinized by the system, what is the probability that the person selected is actually a future terrorist? Also explain if the value of this probability makes you uncomfortable about using a surveillance system? Explain.
An Insurance Company found that only 0.01% of the population is involved in a certain type of accident each year. If its 1000 policyholders were randomly selected from the population what is the probability that knows more than 2 of its clients are involved in such accidents next year.
A recent survey shows that 16% of college students have dogs and 38% have an HBO subscription. Assuming these two events are independent, what is the probability that a randomly selected college student has neither a dog nor HBO?
A manufacturer of laptops reports that among a shipment of 5000 sent to a local distributor, 1000 are slightly defective. If one purchases 10 of these laptops at random from the distributor, what is the probability that exactly 3 are slightly defective?
One student is selected at random from a group of 200 known to consist of 140 full-time (80 female and 60 male) student and 60 part-time (40 female and 20 male) students. Event A is "the student selected is full-time" and event C is "the student selected is female". (a) Are events A and C independent? (b) Find the probability of one student selected is full-time, that should be female.
Suppose that 55% of all adults regularly consume coffee, 45% regularly consume carbonated soda, and 70% regularly consume at least one of these two products. (a) What is the probability that a randomly selected adult regularly consumes both coffee and soda? (b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?
Suppose that 50% of all adults regularly consume coffee, 40% regularly consume carbonated soda, and 65% regularly consume at least one of these two products. (a) What is the probability that a randomly selected adult regularly consumes both coffee and soda? (b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?
1. (a) In a population, 4% of the women are pregnant. A particular home pregnancy test comes back positive for a pregnant woman 95% of the time. However, this test comes back positive even though the woman is not pregnant 5% of the time. i. A woman who is not pregnant takes the test. What is the probability that the test will come back negative? ii. What is the probability that a randomly selected woman tests positive for pregnancy? iii. What is the probability that a randomly selected woman who tested pos- itive for pregnancy is actually pregnant?
With regards to a particular gene, the percentage of genotypes AA, Aa, and aa in a particular population are respectively, 60%, 30%, and 10%. Furthermore, the percentages of these genotypes that contract a certain disease are respectively. 1%, 5% and 20%. If a person does contract the disease, what is the probability that the person is of genotype AA?

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