Suppose you are answering a multiple-choice problem on a exam, and have to choose one ofn options (exactly one of which is correct). Let K = the event that you know the answer,and R = the event that you get the problem right. Suppose that if you know the right answer, you will definitely getthe problem right, but if you do not know, then you will guess completely randomly. LetP (K) = some probability p.(a) Find P (K|R) (in terms of p and n).(b) Prove that P (K|R) ≥ p, and give a more intuitive explanation for why thisis true.(c) When (if ever) does P (K|R) equal p?
Suppose you are answering a multiple-choice problem on a exam, and have to choose one ofn options (exactly one of which is correct). Let K = the event that you know the answer,and R = the event that you get the problem right. Suppose that if you know the right answer, you will definitely getthe problem right, but if you do not know, then you will guess completely randomly. LetP (K) = some probability p.(a) Find P (K|R) (in terms of p and n).(b) Prove that P (K|R) ≥ p, and give a more intuitive explanation for why thisis true.(c) When (if ever) does P (K|R) equal p?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 21E
Related questions
Question
Suppose you are answering a multiple-choice problem on a exam, and have to choose one of
n options (exactly one of which is correct). Let K = theevent that you know the answer,
and R = the event that you get the problem right. Suppose that if you know the right answer, you will definitely get
the problem right, but if you do not know, then you will guess completely randomly. Let
P (K) = someprobability p.
(a) Find P (K|R) (in terms of p and n).
(b) Prove that P (K|R) ≥ p, and give a more intuitive explanation for why this
is true.
(c) When (if ever) does P (K|R) equal p?
n options (exactly one of which is correct). Let K = the
and R = the event that you get the problem right. Suppose that if you know the right answer, you will definitely get
the problem right, but if you do not know, then you will guess completely randomly. Let
P (K) = some
(a) Find P (K|R) (in terms of p and n).
(b) Prove that P (K|R) ≥ p, and give a more intuitive explanation for why this
is true.
(c) When (if ever) does P (K|R) equal p?
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