Question

40. You want to play your one-time-lifetime amount of $5000 in either the Mega Millions or the Illinois Lotto. The probability of winning the Mega Millions with one dollar is 1 and the 135,145,920 minimum prize is $10,000,000. The probability of winning the Illinois Lotto with one dollar is and the minimum prize is $2,000,000. Calculate the expected value of game to 5,089,630 determine which lottery should you play if each game is paying the minimum prize?

could it be explained in simplified terms, I'm a bit confused by the wording

Answer 1

The Expected value of given discrete random values is sum of the [Probability of (outcome) * outcome]

So Expected value  $E(x) = \sum_{i=1}^{n} P(x_{i})*(x_{i})$ where $x_{i}$ is outcome , P($x_{i}$) is probability of $x_{i}$ outcome.

Here is the probability distribution with minimum cash prizes and their product.  

Lottery Name	x ( Min. Cash Prize in $)	P(x)	Product, EV = x * P(x)
Mega Millions	1,00,00,000	=1/135,145,920=0.0000000074	0.073994095
Illinois Lotto	20,00,000	=1/5,089,630=0.0000001965	0.392955873

So the expected cash prize from each ticket of $1,

For Mega Millions is , 0.073994095

and for Illionois Lotto is , 0.392955873

Hence for each 1$ of lottery ticket, expected profit = profit expected from each ticket - 1 ticket cost

For Mega Millions , Expected Profit =  0.073994095 - $1 = -0.926005905

For Illionois Lotto, Expected Profit = 0.392955873 - $1 = -0.607044127

Hence, probability of Expected Profit is more more with Illionois Lotto lottery ( -0.607044127) in comparison to Mega Millions ( -0.926005905) . Hence, we should prefer to play Illionois Lotto lottery , as chances of winning there are more there.