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?
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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