Math Problem Statement
Question 1 Billy purchases one 6-49 lottery ticket every week and keeps track of
the number of “matches”” he has on each of his tickets. To be clear, a “match”
will occur when a number on his ticket matches a number that appears in the
winning combination. A random variable X that keeps track of the number
of matching numbers Billy experiences per week has the probability distribu-
tion function with a mean and standard deviation of P(X=x)=(6x)(436−x)(496)
x=0,1,2,3,4,5,6. E(X)=muX=3649=0.7347 SD(X)=sigmaX=0.75998=0.76 Billy
claims that in a year (52 weeks), on average, he manages to have at least one
matching number on his 6-49 ticket. What do you think about Billy’s claim?
Provide a brief commentary about Billy’s claim using your current knowledge of
statistics and probability theory.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability Theory
Expected Value
Binomial Distribution
Formulas
E(Total Matches in a Year) = 52 × μ_X
P(X = 0)
P(at least one match in 52 weeks) = 1 - P(no matches in all 52 weeks)
Theorems
Expected Value Theorem
Binomial Probability Theorem
Suitable Grade Level
Grades 11-12
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