1. In a group of 100 men, 55 are clean-shaven, 30 have beards and moustaches, 10 have moustaches only, and 5 have beards only. One man is selected at random. (a) What is the probability that the man has a beard? (b) If it is known that the selected man has a beard, what is the probability that he has a moustache? (c) In this group of 100 men, are the events of having a beard and having a moustache independent for a randomly selected man?
1. In a group of 100 men, 55 are clean-shaven, 30 have beards and moustaches, 10 have moustaches only, and 5 have beards only. One man is selected at random. (a) What is the probability that the man has a beard? (b) If it is known that the selected man has a beard, what is the probability that he has a moustache? (c) In this group of 100 men, are the events of having a beard and having a moustache independent for a randomly selected man?
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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![1. In a group of 100 men, 55 are clean-shaven, 30 have beards and moustaches, 10 have moustaches
only, and 5 have beards only. One man is selected at random.
(a) What is the probability that the man has a beard?
(b) If it is known that the selected man has a beard, what is the probability that he has a moustache?
(c) In this group of 100 men, are the events of having a beard and having a moustache independent
for a randomly selected man?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1652026a-6ba6-42d7-9e35-ad3e7516e1ec%2F6ecdeec9-1cbb-4f36-bc04-fd7d3275f9ec%2F470nwyn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. In a group of 100 men, 55 are clean-shaven, 30 have beards and moustaches, 10 have moustaches
only, and 5 have beards only. One man is selected at random.
(a) What is the probability that the man has a beard?
(b) If it is known that the selected man has a beard, what is the probability that he has a moustache?
(c) In this group of 100 men, are the events of having a beard and having a moustache independent
for a randomly selected man?
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Step 1: Define the data to obtain the probability that the man has a beard.
VIEWStep 2: calculate the probability
VIEWStep 3: Obtain the probability that the randomly selected man has a moustache given that he has beard.
VIEWStep 4: Determine whether the events beard and having a moustache are independent or not.
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