sm8_43

Prévia do material em texto

Problem 8.43 The probability that an event occurs at least once in four independent trials is equal to 
0.59. What is the probability of occurrence of the event in one trial, if the probabilities are equal in all 
trials? 
 
Solution 
The probability that the event occurs on a least one trial is 1 minus the probability that the 
event does not occur at all. Let p be the probability of occurrence on a single trial, so 1-p 
is the probability of not occurring on a single trial. Then 
 [ ] ( )
4
4
)1(159.0
11occurenceoneleastat
p
p
−−=
−−=P
 
 
Solving for p gives a probability on a single trial of 0.20. 
 
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only 
to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that 
permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. 
page…8-53