Math Problem Statement

give me r code for

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 distribution

function with a mean and standard deviation of

푃 (푋 = 푥) =

(

6

)(

43

6−푥

)

(

49

6

)

x = 0, 1, 2, 3, 4, 5, 6

퐸[푋] = 휇

=

36

49

= 0.7347

푆퐷(푋) = 휎

= 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
Combinatorics
Expected Value
Simulation

Formulas

P(X = x) = (C(6, x) * C(43, 6 - x)) / C(49, 6)
Expected number of weeks = P(X ≥ 1) * 52

Theorems

Binomial Distribution
Law of Large Numbers

Suitable Grade Level

Grades 11-12