Mathematics, 15.10.2019 04:00, estermartinez
An urn contains four balls numbered 1 through 4. the balls are selected one at a time without replacement. a match occurs if the ball numbered m is the mth ball selected. let the event
ai
denote a match on the ith draw, i = 1, 2, 3, 4. a. show that
p(ai)=3! /4!
for each i. b. show that
p(ai∩aj)=2! /4! ,i≠j
. c. show that
p(ai∩aj∩ak)=1! /4! ,i≠j, i≠k, j≠k
. d. show that the probability of at least one match is
p(a1∪a2∪a3∪a4)=1−1/2! +1/3! −1/4!
. e. extend this exercise so that there are n balls in the urn. show that the probability of at least one match is
p(a1∪a2∪⋅⋅⋅∪an)
,
=1−1/2! +1/3! −1/4! +⋅⋅⋅+(−1)n+1/n!
,
=1−(1−1/1! +1/2! −1/3! +⋅⋅⋅+(−1)n/n! )
. f. what is the limit of this probability as n increases without bound?
Answers: 2
Mathematics, 21.06.2019 21:00, mccdp55
Select the correct answer from each drop-down menu. a system of equations and its solution are given below. system a complete the sentences to explain what steps were followed to obtain the system of equations below. system b to get system b, the equation in system a was replaced by the sum of that equation and times the equation. the solution to system b the same as the solution to system a.]
Answers: 1
An urn contains four balls numbered 1 through 4. the balls are selected one at a time without replac...
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