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7. The coefficients of the quadratic equation x² + bx + c = 0 are determined by tossing a fair die twice, the first outcome to determine b and second to determine c. What is the probability that the equation has real root (s), i.e., what is the probability that the discriminant b² - 4c ≥ 0 ? 8. A number is selected at random from the set {1, 2, 3, ..., 1000}. What is the probability that it is divisible by 19? 9. A number is selected at random from the set {1, 2, 3, ..., 1000}. What is the probability that it is not divisible by 3 or 5? 10. Two people are riding an elevator that can stop at floors two, three,...., and N. What is the probability that they will get off at different floors? 11. A person has 10 physics and 4 chemistry books (all books are distinct). In how many ways can the books be arranged if all the physics books are to be together and all the chemistry books are to be together? 12. A researcher wants to compare three different types of diets, say, A, B, and C. Each is used on four people (so, you may have AAAABBBBCCCC, ABACABACBBCC, etc). In how many different ways can this be done?

7. The coefficients of the quadratic equation x² + bx + c = 0 are determined by tossing a fair die twice, the first outcome to determine b and second to determine c. What is the probability that the equation has real root (s), i.e., what is the probability that the discriminant b² - 4c ≥ 0 ? 8. A number is selected at random from the set {1, 2, 3, ..., 1000}. What is the probability that it is divisible by 19? 9. A number is selected at random from the set {1, 2, 3, ..., 1000}. What is the probability that it is not divisible by 3 or 5? 10. Two people are riding an elevator that can stop at floors two, three,...., and N. What is the probability that they will get off at different floors? 11. A person has 10 physics and 4 chemistry books (all books are distinct). In how many ways can the books be arranged if all the physics books are to be together and all the chemistry books are to be together? 12. A researcher wants to compare three different types of diets, say, A, B, and C. Each is used on four people (so, you may have AAAABBBBCCCC, ABACABACBBCC, etc). In how many different ways can this be done?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 15E
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I need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)

7. The coefficients of the quadratic equation x² + bx + c = 0 are determined by tossing a fair die twice, the first outcome to determine b and second to determine c. What is the probability that the equation has real root (s), i.e., what is the probability that the discriminant b² - 4c ≥ 0 ? 8. A number is selected at random from the set {1, 2, 3, ..., 1000}. What is the probability that it is divisible by 19? 9. A number is selected at random from the set {1, 2, 3, ..., 1000}. What is the probability that it is not divisible by 3 or 5?
Transcribed Image Text:7. The coefficients of the quadratic equation x² + bx + c = 0 are determined by tossing a fair die twice, the first outcome to determine b and second to determine c. What is the probability that the equation has real root (s), i.e., what is the probability that the discriminant b² - 4c ≥ 0 ? 8. A number is selected at random from the set {1, 2, 3, ..., 1000}. What is the probability that it is divisible by 19? 9. A number is selected at random from the set {1, 2, 3, ..., 1000}. What is the probability that it is not divisible by 3 or 5?
10. Two people are riding an elevator that can stop at floors two, three,...., and N. What is the probability that they will get off at different floors? 11. A person has 10 physics and 4 chemistry books (all books are distinct). In how many ways can the books be arranged if all the physics books are to be together and all the chemistry books are to be together? 12. A researcher wants to compare three different types of diets, say, A, B, and C. Each is used on four people (so, you may have AAAABBBBCCCC, ABACABACBBCC, etc). In how many different ways can this be done?
Transcribed Image Text:10. Two people are riding an elevator that can stop at floors two, three,...., and N. What is the probability that they will get off at different floors? 11. A person has 10 physics and 4 chemistry books (all books are distinct). In how many ways can the books be arranged if all the physics books are to be together and all the chemistry books are to be together? 12. A researcher wants to compare three different types of diets, say, A, B, and C. Each is used on four people (so, you may have AAAABBBBCCCC, ABACABACBBCC, etc). In how many different ways can this be done?
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