Two shopkeepers run their business at Nagoya. Shop K sells fish soup, and Shop N sells Sushi. They run their business based on weather condition. Let K, N denote the event where Shop K, N are on business (on a particular day) respectively. The (conditional) probabilities of whether they open the shop is given in the following table. From the statistics, for a single day it has probability 0.5, 0.2, 0.3 to be sunny, cloudy and rainy respectively. Weather KN KN° K N K Nc Sunny Cloudy 0.45 0.25 0.20 0.10 0.50 0.15 0.20 0.15 Rainy 0.05 0.15 0.30 0.50 (a)What is the probability that it is rainy today, and Shop K is open? (b) Find P(Κ), P(N), P(KN), P(Κυ Ν). (c) If Reo recalls on 2019/4/15 he had fish soup and sushi at Nagoya. What is the probability that it was a cloudy day?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Two shopkeepers run their business at Nagoya. Shop K sells fish soup,
and Shop N sells Sushi. They run their business based on weather
condition. Let K, N denote the event where Shop K, N are on business
(on a particular day) respectively. The (conditional) probabilities of
whether they open the shop is given in the following table. From the
statistics, for a single day it has probability 0.5, 0.2, 0.3 to be sunny,
cloudy and rainy respectively.
Weather
KN
KN°
K N K Nc
Sunny
Cloudy
Rainy
0.45
0.25
0.20
0.10
0.50
0.15
0.20
0.15
0.05
0.15
0.30
0.50
(a)What is the probability that it is rainy today, and Shop K is open?
(b) Find P(Κ), P(N), P(KN), P(Κυ Ν).
(c) If Reo recalls on 2019/4/15 he had fish soup and sushi at Nagoya.
What is the probability that it was a cloudy day?
Transcribed Image Text:Two shopkeepers run their business at Nagoya. Shop K sells fish soup, and Shop N sells Sushi. They run their business based on weather condition. Let K, N denote the event where Shop K, N are on business (on a particular day) respectively. The (conditional) probabilities of whether they open the shop is given in the following table. From the statistics, for a single day it has probability 0.5, 0.2, 0.3 to be sunny, cloudy and rainy respectively. Weather KN KN° K N K Nc Sunny Cloudy Rainy 0.45 0.25 0.20 0.10 0.50 0.15 0.20 0.15 0.05 0.15 0.30 0.50 (a)What is the probability that it is rainy today, and Shop K is open? (b) Find P(Κ), P(N), P(KN), P(Κυ Ν). (c) If Reo recalls on 2019/4/15 he had fish soup and sushi at Nagoya. What is the probability that it was a cloudy day?
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