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?
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
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
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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