Professor Nowotny likes to cook. He cuts his potatoes into thin slices and fries them in a pan. He puts them in and occasionally tosses them. At each toss the potato slices fall independently of each other with pr the same side and probability 1-p onto the other side. Q1: For n slices, what is the probability that they all fall back onto the same side in a single toss? A p" B1-p" C n p Dn (1-p) E (1-P)" [Select] Q2: He has n slices and tosses k times. What is the probability that all slices have both sides fried, i.e. have fallen at least once on the other side? Ak-p" Bn p C (1-p") D (1-pk)n E (1-p)nk [Select] v Q3: Professor Nowotny has n slices in the pan and would like to have them all fried on both sides with probability >99%. How many times k does he need to toss at least? log(0.01) Ek D KZ log(P) log (1-(0.01)") log(p) C kz log(1-(0.99)/") log(p) log((0.99)¹/) log(p) A k2 [Select] V B k> log(1-(0.99)¹/") log(1-p)
Professor Nowotny likes to cook. He cuts his potatoes into thin slices and fries them in a pan. He puts them in and occasionally tosses them. At each toss the potato slices fall independently of each other with pr the same side and probability 1-p onto the other side. Q1: For n slices, what is the probability that they all fall back onto the same side in a single toss? A p" B1-p" C n p Dn (1-p) E (1-P)" [Select] Q2: He has n slices and tosses k times. What is the probability that all slices have both sides fried, i.e. have fallen at least once on the other side? Ak-p" Bn p C (1-p") D (1-pk)n E (1-p)nk [Select] v Q3: Professor Nowotny has n slices in the pan and would like to have them all fried on both sides with probability >99%. How many times k does he need to toss at least? log(0.01) Ek D KZ log(P) log (1-(0.01)") log(p) C kz log(1-(0.99)/") log(p) log((0.99)¹/) log(p) A k2 [Select] V B k> log(1-(0.99)¹/") log(1-p)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Professor Nowotny likes to cook. He cuts his potatoes into thin slices and fries them in a pan. He puts them in and occasionally tosses them. At each toss the potato slices fall independently of each other with probability ponto
the same side and probability 1-p onto the other side.
Q1: For n slices, what is the probability that they all fall back onto the same side in a single toss?
A p
B 1-p"
с п.р Dn (1-P)
E (1-p)"
[Select]
Q2: He has n slices and tosses k times. What is the probability that all slices have both sides fried, i.e. have fallen at least once on the other side?
Ak p
Bn.pk C (1-p¹) k D (1-pk)n E (1-p)nk
[Select]
Q3: Professor Nowotny has n slices in the pan and would like to have them all fried on both sides with probability > 99%. How many times k does he need to toss at least?
log (1-(0.99)¹/n)
log(p)
log((0.99)¹/")
log(p)
D k>
log(1-(0.99)¹/n)
log(1-p)
A k2
[Select]
B k>
log(1-(0.01)")
log(p)
CkZ
E k>
1 log(0.01)
log(p)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a6b1bc8-8284-4cba-9dcf-cfbeea478688%2F9389fdef-978d-4299-9248-9d6d70f4799f%2Frsd8788_processed.png&w=3840&q=75)
Transcribed Image Text:Professor Nowotny likes to cook. He cuts his potatoes into thin slices and fries them in a pan. He puts them in and occasionally tosses them. At each toss the potato slices fall independently of each other with probability ponto
the same side and probability 1-p onto the other side.
Q1: For n slices, what is the probability that they all fall back onto the same side in a single toss?
A p
B 1-p"
с п.р Dn (1-P)
E (1-p)"
[Select]
Q2: He has n slices and tosses k times. What is the probability that all slices have both sides fried, i.e. have fallen at least once on the other side?
Ak p
Bn.pk C (1-p¹) k D (1-pk)n E (1-p)nk
[Select]
Q3: Professor Nowotny has n slices in the pan and would like to have them all fried on both sides with probability > 99%. How many times k does he need to toss at least?
log (1-(0.99)¹/n)
log(p)
log((0.99)¹/")
log(p)
D k>
log(1-(0.99)¹/n)
log(1-p)
A k2
[Select]
B k>
log(1-(0.01)")
log(p)
CkZ
E k>
1 log(0.01)
log(p)
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