Answered: 5. The probability that at least one of…

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

5. The probability that at least one of the events A and B will occur is P(A ∪ B) = P(A) + P(B) −
P(A ∩ B). Find the probability that exactly one of the events A and B will occur.

Expert Solution

Step 1: Given that

$A space colon space e v e n t space A B space colon space e v e n t space B$ $left square bracket A space & space B space a r e space i n d e p e n d e n t space e v e n t s right square bracket$

$table row blank blank cell therefore space P left parenthesis A right parenthesis space a n d space P left parenthesis B right parenthesis space b e space t h e space p r o b a b i l i t i e s space o f space e v e n t s space A space a n d space B space r e s p e c t i v e l y. end cell row blank blank cell space space end cell end table$

and $table row cell therefore space P left parenthesis A to the power of c right parenthesis space end cell equals cell 1 minus P left parenthesis B to the power of c right parenthesis end cell row cell & space P left parenthesis B to the power of c right parenthesis space end cell equals cell 1 minus P left parenthesis A to the power of c right parenthesis end cell end table$