Question
Asked Feb 12, 2019
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One state lottery has 1,100 prizes of $1; 140 prizes of $10; 25 prizes of $60; 5 prizes of $290; 2 prizes of $1,080; and 1 prize of $2,800. Assume that 21,000 lottery tickets are issued
and sold for $1.
Question 3
What is the lottery's expected profit per ticket?
Question 4
What is the lottery's standard deviation of profit per ticket?
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One state lottery has 1,100 prizes of $1; 140 prizes of $10; 25 prizes of $60; 5 prizes of $290; 2 prizes of $1,080; and 1 prize of $2,800. Assume that 21,000 lottery tickets are issued and sold for $1. Question 3 What is the lottery's expected profit per ticket? Question 4 What is the lottery's standard deviation of profit per ticket?

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Expert Answer

Step 1

Given total lottery tickets sold 21,000 per $1 each.

Number of $1 prizes = 1100

Number of $10 prizes = 140

Number of $60 prizes = 25

Number of $290 prizes = 5

Number of $1080 prizes = 2

Number of $2800 prizes = 1

Here the tickets are classified into ticket which won $1,$10, $60, $290, $1080, $2800 and won nothing. The number of tickets in each category is shown below in a table

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Step 2

Profit obtained by selling $1 prize lottery ticket = ticket prize - prize money = 1-1 = 0

Profit obtained by selling  $10 prize lottery ticket = ticket prize - prize money = 1-10 = -9

Profit obtained by selling $60  prize lottery ticket = ticket prize - prize money = 1-60 = -59

Profit obtained by selling $290  prize lottery ticket = ticket prize - prize money = 1-290 = -289

Profit obtained by selling $1080  prize lottery ticket = ticket prize - prize money = 1-10 80= -1079

Profit obtained by selling $2800  prize lottery ticket = ticket prize - prize money = 1-2800 = -2799

Profit obtained by selling no  prize lottery ticket = ticket prize - prize money = 1-0 = 1.

Writing the table in terms of profit obtained per ticket and number of ticket sold given below

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Step 3

The total tickets sold are 21000. So we calculate the probability of profit per each category will be total number of tickets sold/total number of tickets.

For example probability of $0 profit per ticket  = total tickets with 1$ prize/total tickets sold

=1100/...

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