Answered: 6.A sailor does not go to sail if it…

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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Question

6.A sailor does not go to sail if it rains. The probability that it rains one day is 0.1. The Probability that the sailor will go to sail one day is 0.03. If it doesn't rain, what is the probability that it goes to navigate? 7. A waiter in a restaurant attends 2 tables at the same time. In the table there are 5 people, and Santeño, 2 Cocleanos and 2 Colonses. On table B there are 3 people, 1 Santeño, 1 Coclean and 1 Colonense The waiter forgets the order of 1 Santeño. What is the probability that is the Santeño From the table a?

Expert Solution

Step 1: Finding the probability that it goes to navigate

Problem 6:

The probability that it rains one day is $P not stretchy left parenthesis text rain end text not stretchy right parenthesis equals 0.1$ .

The probability that the sailor will go to sail one day is $P not stretchy left parenthesis text sail end text not stretchy right parenthesis equals 0.03$ .

The probability that it doesn't rain is $P not stretchy left parenthesis text no rain end text not stretchy right parenthesis equals 1 minus P not stretchy left parenthesis text rain end text not stretchy right parenthesis equals 1 minus 0.1 equals 0.9$ .

The probability that the sailor will go to sail given that it doesn't rain is the conditional probability $P not stretchy left parenthesis text sail end text not stretchy vertical line text no rain end text not stretchy right parenthesis$ , which we can calculate using Bayes' theorem:

$P not stretchy left parenthesis text sail end text not stretchy vertical line text no rain end text not stretchy right parenthesis equals fraction numerator P not stretchy left parenthesis text no rain end text not stretchy vertical line text sail end text not stretchy right parenthesis cross times P not stretchy left parenthesis text sail end text not stretchy right parenthesis over denominator P not stretchy left parenthesis text no rain end text not stretchy right parenthesis end fraction$

Since if it doesn't rain, the sailor will go to sail ( $P not stretchy left parenthesis text no rain end text not stretchy vertical line text sail end text not stretchy right parenthesis equals 1$ ), we have:

$P not stretchy left parenthesis text sail end text not stretchy vertical line text no rain end text not stretchy right parenthesis equals fraction numerator 1 cross times 0.03 over denominator 0.9 end fraction$

$P not stretchy left parenthesis text sail end text not stretchy vertical line text no rain end text not stretchy right parenthesis almost equal to 0.0333$ (approximately)

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