Medicine. A laboratory technician is to be tested on identifying blood types from 8 standard classifications. (A) If 3 distinct samples are chosen at random from the 8 types and if the technician is not allowed to repeat any answers, what is the probability that all 3 could be correctly identified by just guessing? (B) If repeats are allowed in the 3 blood types chosen at random from the 8 and if the technician is allowed to repeat answers, what is the probability that all 3 are identified correctly by just guessing?
Medicine. A laboratory technician is to be tested on identifying blood types from 8 standard classifications. (A) If 3 distinct samples are chosen at random from the 8 types and if the technician is not allowed to repeat any answers, what is the probability that all 3 could be correctly identified by just guessing? (B) If repeats are allowed in the 3 blood types chosen at random from the 8 and if the technician is allowed to repeat answers, what is the probability that all 3 are identified correctly by just guessing?
Solution Summary: The author calculates the probability that all 3 samples of blood types chosen from 8 could be correctly identified by guessing, if the technician is not allowed to repeat the answers.
Medicine. A laboratory technician is to be tested on identifying blood types from
8
standard classifications.
(A) If
3
distinct samples are chosen at random from the
8
types and if the technician is not allowed to repeat any answers, what is the probability that all
3
could be correctly identified by just guessing?
(B) If repeats are allowed in the
3
blood types chosen at random from the
8
and if the technician is allowed to repeat answers, what is the probability that all
3
are identified correctly by just guessing?
Refer to page 3 for stability in differential systems.
Instructions:
1.
2.
Analyze the phase plane of the system provided in the link to determine stability.
Discuss the role of Lyapunov functions in proving stability.
3.
Evaluate the impact of eigenvalues of the Jacobian matrix on the nature of equilibria.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]
Refer to page 10 for properties of Banach and Hilbert spaces.
Instructions:
1. Analyze the normed vector space provided in the link and determine if it is complete.
2.
Discuss the significance of inner products in Hilbert spaces.
3.
Evaluate examples of Banach spaces that are not Hilbert spaces.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]
Refer to page 1 for eigenvalue decomposition techniques.
Instructions:
1.
Analyze the matrix provided in the link to calculate eigenvalues and eigenvectors.
2. Discuss how eigenvalues and eigenvectors are applied in solving systems of linear equations.
3.
Evaluate the significance of diagonalizability in matrix transformations.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]
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