i-th house in her neighborhood. At any house that she visits, either: s at the house and answers the door; this happens with probability q (where 0 < a picture of her hometown; at the house and Amy returns home. hat the collection of all events of the form {Amy stays home on day i} and {Somed 2,..., are (mutually) independent. s the probability that Amy gives out a picture on the first day? me integers k and n, with n ≥ 1 and 0 ≤ k ≤n. s the probability that she gave out exactly k pictures on the first n days? s the probability that she stayed home on day 1, given that she did not give out a the first week (7 days), what is the probability that there were no days in which A picture of her hometown? cation (June 13): What is the probability that there were no days in event A happe axinline]A[/mathjaxinline>] is that Amy went out but did not give out a picture of
i-th house in her neighborhood. At any house that she visits, either: s at the house and answers the door; this happens with probability q (where 0 < a picture of her hometown; at the house and Amy returns home. hat the collection of all events of the form {Amy stays home on day i} and {Somed 2,..., are (mutually) independent. s the probability that Amy gives out a picture on the first day? me integers k and n, with n ≥ 1 and 0 ≤ k ≤n. s the probability that she gave out exactly k pictures on the first n days? s the probability that she stayed home on day 1, given that she did not give out a the first week (7 days), what is the probability that there were no days in which A picture of her hometown? cation (June 13): What is the probability that there were no days in event A happe axinline]A[/mathjaxinline>] is that Amy went out but did not give out a picture of
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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![Amy immigrated to a new city, and would like to make friends with her new neighbours.
On any particular day i, she feels shy with probability 1 − p (0 < p < 1) and stays home; or, with probability p, she goes out
and visits the i-th house in her neighborhood. At any house that she visits, either:
(i) someone is at the house and answers the door; this happens with probability q (where 0 < g < 1). In that case, Amy
shows them a picture of her hometown;
(ii) no one is at the house and Amy returns home.
We assume that the collection of all events of the form {Amy stays home on day i} and {Someone is at the i-th house on day
i}, for i = 1, 2, . . ., are (mutually) independent.
1. What is the probability that Amy gives out a picture on the first day?
2. Fix some integers k and n, with n ≥ 1 and 0 ≤k ≤n.
What is the probability that she gave out exactly k pictures on the first n days?
3. What is the probability that she stayed home on day 1, given that she did not give out a picture on that day?
4. Within the first week (7 days), what is the probability that there were no days in which Amy went out but did not give
out a picture of her hometown?
Clarification (June 13): What is the probability that there were no days in event A happens, where event
[mathjaxinline]A[/mathjaxinline>] is that Amy nt out but did not give out a picture of her hometown?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c43a342-7a5b-418b-9a27-ab755687fb42%2F4d8db9a7-2fd7-4078-a329-21114d8f8f31%2Fx47v3er_processed.png&w=3840&q=75)
Transcribed Image Text:Amy immigrated to a new city, and would like to make friends with her new neighbours.
On any particular day i, she feels shy with probability 1 − p (0 < p < 1) and stays home; or, with probability p, she goes out
and visits the i-th house in her neighborhood. At any house that she visits, either:
(i) someone is at the house and answers the door; this happens with probability q (where 0 < g < 1). In that case, Amy
shows them a picture of her hometown;
(ii) no one is at the house and Amy returns home.
We assume that the collection of all events of the form {Amy stays home on day i} and {Someone is at the i-th house on day
i}, for i = 1, 2, . . ., are (mutually) independent.
1. What is the probability that Amy gives out a picture on the first day?
2. Fix some integers k and n, with n ≥ 1 and 0 ≤k ≤n.
What is the probability that she gave out exactly k pictures on the first n days?
3. What is the probability that she stayed home on day 1, given that she did not give out a picture on that day?
4. Within the first week (7 days), what is the probability that there were no days in which Amy went out but did not give
out a picture of her hometown?
Clarification (June 13): What is the probability that there were no days in event A happens, where event
[mathjaxinline]A[/mathjaxinline>] is that Amy nt out but did not give out a picture of her hometown?
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