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,](//img.homeworklib.com/images/c171944c-e3d8-4e59-b64a-997a6d09a5af.png?x-oss-process=image/resize,w_560)
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](//img.homeworklib.com/images/9a4ef54c-d5e8-40d7-9bd9-16ab353a812d.png?x-oss-process=image/resize,w_560)
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,](//img.homeworklib.com/images/248d95c7-8227-4df2-b356-df119767dde6.png?x-oss-process=image/resize,w_560)
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 1б](//img.homeworklib.com/images/301b3ac8-ca21-4846-9789-48d5380492ae.png?x-oss-process=image/resize,w_560)
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](//img.homeworklib.com/images/52a69140-d5c2-4b90-a1ff-0228af3f8a87.png?x-oss-process=image/resize,w_560)
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 10](//img.homeworklib.com/images/c3499e1a-cba9-4eac-b6fd-62f2579929a9.png?x-oss-process=image/resize,w_560)
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
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
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
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
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)
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