Question

PROBABILITY DISTRIBUTION AND EXPECTED VALUE QUESTION
An online gambling site offers a first prize of $50,000 and two second prizes of $10,000 each for registered users when they place a bet. A random bet will be selected over a 24-hour period. One million bets are received in the contest. Find the expected winnings if you can place one registered bet of $1 in the given period. @satellite73

Answer 1

this is easy to do if we think this way
buy up all the tickets, you spend \(\$1,000,000\)

Answer 2

you get back a total of \(\$500,000+2\times \$10,000=\$520,000\)

Answer 3

it is 50000 not 500000

Answer 4

oh even worse

Answer 5

you get a back a total of \(50,000+20,000=70,000\) for a net loss of \[1,000,000-70,000= -930000\]

Answer 6

averaged over the one million tickets your loss per ticket is
\[-.93\]

Answer 7

ok.sure we not done right.lol

Answer 8

@satellite73

Answer 9

no we are done

Answer 10

your expected value is \(-.93\) i.e. you expect to lose 93 cents for every one dollar ticket you buy

Answer 11

so u divided the -9300000 by 1000000 to get -.93 right?

Answer 12

yes

Answer 13

well actually it is \(-930,000\) divided by \(1,000,000\)

Answer 14

Or, for n = 1,000,000, we have

\(\left(\dfrac{1}{n}\cdot 50000\right) + \left(\dfrac{2}{n}\cdot 10000\right) + \left(\dfrac{n-3}{n}\cdot 0\right) - 1 = 0.93\),

wonderfully the same correct solution.

Answer 15

Did it again! -0.93!

Answer 16

are ur last figures in parentheses multiplied by 0

Answer 17

@tkhunny

Answer 18

or even
\[49,999\times \frac{1}{1,000,000}+9,999\times \frac{2}{1,000,000}-1\times \frac{999,9997}{1,000,000}\]

Answer 19

but i always think it is easier to do it the first way
less confusing for me

Answer 20

Yes, multiplied by zero. This is just the piece that represents winning nothing. You just gave them your dollar! Obviously, this term could have been omitted.

Answer 21

or "the sum of the amount you win times the probability you win it"

Answer 22

Thoroughly agree @satellite73 !! There are several ways to proceed. The fundamental principles are the same. For a learning exercise, I would ALWAYS try more than one way to achieve the same answer.

Answer 23

so the -1 represents the $1 right ?

Answer 24

Right. This is particularly clear in @satellite73's last version.

49999 = 50000 - 1
9999 = 10000 - 1

There's that dollar that you have to pay just to get in the game.

Answer 25

perfect