Question

To get full credits for the project, you must: 1) Turn in the project on time. One point will be deducted for "each day" (including weekends and holidays) that the project is late. 2) State the goal (or the problem) of the project 3) State the process, including EXCEL commands used. 4) State the results. Go to New York Lottery website: https://www.megamillions.com/how-to-play Use the information on Mega Millions to do the following: a) Let X be the random variable which represents the amount of wining when $2 (1 ticket) is played. What are the possible values for X? Assume Jackpot is $200 million. b) Find the probability of winning Mega Millions at each prize level. (Use chances of winning posted on the website to determine the probabilities) Construct the probability distribution for the amount of winning in Mega Millions. c) Find the expected winning (expected value) in Mega Millions. Show Excel formulas for the calculations.

Answer 1

Solution:

We use the following table from the website

Match Chances Prize Jackpot $1,000,000 $10,000 $500 $200 510 $10 $4 $2 1 in 302,575,350 1 in 12,607,306 1 in 931,001 1 in 38,792 1 in 14,547 1 in 606 1 in 693 1 in 89 1 in 37 Overall chances of winning any prize 1 in 24

a) X is a random variable which represents the amount of winning when 1 ticket is played.

The possible values of X are 200,000,000, 1,000,000, 10,000, 500, 200, 10, 4, 2

b) Based on the chances of winning posted, we can make the following table in excel

1 Amount of Winning (X) Chances of winning (1 in) 302575350 12607306 931001 38792 14547 606 693 89 37 Probability of winning 1/B2 1/B3 1/B4 1/B5 1/B6 3 1000000 4 10000 5 500 6 200 7 10 8 10 9 4 10 2 =1/88 -1/B10

get these values

Amount of Chances of 1 Winning (X) winning (1 inwinning Probability of 2 $200,000,000 3 $ 1,000,000 10,000 500 200 10 10 302,575,350 0.000000003 12,607,306 0.000000079 931,001 0.000001074 38,792 0.000025779 14,547 0.000068743 606 0.001650165 693 0.001443001 89 0.011235955 37 0.027027027 10

To get the probability distribution of X we need to combine the 2 probabilities for winning X=$10.We get the following

P(X=x) S 200,000,000 0.000000003 S 1,000,000 0.000000079 S 10,000 0.000001074 500 0.000025779 200 0.000068743 101 0.003093 1бб 4 0.011235955 2 0.027027027

The above is the probability distribution for the amount of winning in Mega Millions

c) The expected value is calculated as

200000000 × P(X-200000000) 1000000 × P(X = 1000000)+ 10000 × P(X 10000) + 500 × P(X 500)+ 200 × P(X 200) 10 × P(X 10)4 × P(X = 4) 2 × P(X 2)

we show the above calculation the following excel

Amount of Winning sof Probability Inning (1 In 302575350 12607306 931001 of winnin 1/B3 =1/B5 x-x E2 F2 1000000 C3 10000 3 1000000 4 10000 5 500 6 200 =1/B7 = 1/B8 1/B9 =1/B10 8 10 9 4 10 2 get these values Amount of Chances of Probability of winning (1 in winni 1 Winnin 2 $200,000,000 302,575,350 0.000000003 3 1,000,00012,607,306 0.000000079 931,001 0.000001074 38,792 0.000025779 14,547 0.000068743 606 0.001650165 693 0.001443001 89 0.011235955 37 0.027027027 $ 200,000,000 0.000000003 0.6610 $ 1,000,000 0.000000079 0.0793 $10,000 0.000001074 0. 4 S10,000 500 0.000025779 2001 0.0000б8743 10 0.003093166 4 0.011235955 2 0.027027027 0.0129 0.0137 0.0309 0.0449 0.0541 10 10 S the expected winning in Mega Millions is $0.91