Mega Millions is one of the most popular lottery games in the United States. Virtually all states participate in Mega Millions. Rules for playing and the list of prizes in most states are given below (see megamillions.com).
Rules:
• Select five numbers from a pool of numbers from 1 to 52 and one Mega Ball number from a second pool of numbers from 1 to 52.
• Each wager costs $1.
Prizes:
• Match all five numbers + Mega Ball-win jackpot (minimum of $12,000,000)
• Match all five numbers-win $250,000
• Match four numbers + Mega Ball-win $10,000
• Match four numbers-win $150
• Match three numbers + Mega Ball-win $150
• Match two numbers + Mega Ball-win $10
• Match three numbers-win $7
• Match one number + Mega Ball-win $3
• Match Mega Ball-win $2
Find the probability of winning
a. The jackpot.
b. The $250,000 prize. (Note that this requires matching all five numbers but not matching the Mega Ball.)
c. $10,000.
d. $150.
e. $10.
f. $7.
g. $3.
h. $2.
i. Nothing.